On the Coding Capacity of Reverse-Complement and Palindromic Duplication-Correcting Codes (2312.00394v2)

Published 1 Dec 2023 in cs.IT and math.IT

Abstract: We derive the coding capacity for duplication-correcting codes capable of correcting any number of duplications. We do so both for reverse-complement duplications, as well as palindromic (reverse) duplications. We show that except for duplication-length $1$, the coding capacity is $0$. When the duplication length is $1$, the coding capacity depends on the alphabet size, and we construct optimal codes.

References (22)

Goldman, N., Bertone, P., Chen, S., Dessimoz, C., LeProust, E.M., Sipos, B., Birney, E.: Towards practical, high-capacity, low-maintenance information storage in synthesized DNA. Nature 494(7435), 77–80 (2013) Shipman et al. [2017] Shipman, S.L., Nivala, J., Macklis, J.D., Church, G.M.: CRISPR-Cas encoding of digital movie into the genomes of a population of living bacteria. Nature 547, 345–349 (2017) Farnoud et al. [2016] Farnoud, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inform. Theory 62(2), 811–824 (2016) Jain et al. [2017] Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Shipman, S.L., Nivala, J., Macklis, J.D., Church, G.M.: CRISPR-Cas encoding of digital movie into the genomes of a population of living bacteria. Nature 547, 345–349 (2017) Farnoud et al. [2016] Farnoud, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inform. Theory 62(2), 811–824 (2016) Jain et al. [2017] Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inform. Theory 62(2), 811–824 (2016) Jain et al. [2017] Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Shipman, S.L., Nivala, J., Macklis, J.D., Church, G.M.: CRISPR-Cas encoding of digital movie into the genomes of a population of living bacteria. Nature 547, 345–349 (2017) Farnoud et al. [2016] Farnoud, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inform. Theory 62(2), 811–824 (2016) Jain et al. [2017] Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inform. Theory 62(2), 811–824 (2016) Jain et al. [2017] Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Farnoud, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inform. Theory 62(2), 811–824 (2016) Jain et al. [2017] Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Jain, S., Farnoud, F., Schwartz, M., Bruck, J.: Duplication-correcting codes for data storage in the DNA of living organisms. IEEE Trans. Inform. Theory 63(8), 4996–5010 (2017) Zeraatpisheh et al. [2019] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of tandem duplication correcting codes. IET Communications 13(15), 2217–2225 (2019) Zeraatpisheh et al. [2020] Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Zeraatpisheh, M., Esmaeili, M., Gulliver, T.A.: Construction of duplication correcting codes. IEEE Access 8, 96150–96161 (2020) Yu and Schwartz [2024] Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Yu, W., Schwartz, M.: On duplication-free codes for disjoint or equal-length errors. arXiv preprint arXiv:2401.04675 (2024) Kovačević [2019] Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Kovačević, M.: Zero-error capacity of duplication channels. IEEE Trans. Communications 67(10), 6735–6742 (2019) Lenz et al. [2019] Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Lenz, A., Wachter-Zeh, A., Yaakobi, E.: Duplication-correcting codes. Designs, Codes and Cryptography 87, 277–298 (2019) Goshkoder et al. [2023] Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Goshkoder, D., Polyanskii, N., Vorobyev, I.: Codes correcting a single long duplication error. In: Proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT2023), Taipei, Taiwan, pp. 2708–2713 (2023) Nguyen et al. [2022] Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Nguyen, T.T., Cai, K., Song, W., Immink, K.A.S.: Optimal single chromosome-inversion correcting codes for data storage in live DNA. In: Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT2022), Espoo, Finland, pp. 1791–1796 (2022) Ben-Tolila and Schwartz [2022] Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Ben-Tolila, E., Schwartz, M.: On the reverse-complement string-duplication system. IEEE Trans. Inform. Theory 68(11), 7184–7197 (2022) Tang et al. [2020] Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Tang, Y., Yehezkeally, Y., Schwartz, M., Farnoud, F.: Single-error detection and correction for duplication and substitution channels. IEEE Trans. Inform. Theory 66(11), 6908–6919 (2020) Tang and Farnoud [2021] Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Tang, Y., Farnoud, F.: Error-correcting codes for short tandem duplication and edit errors. IEEE Trans. Inform. Theory 68(2), 871–880 (2021) Tang et al. [2023] Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Tang, Y., Wang, S., Lou, H., Gabrys, R., Farnoud, F.: Low-redundancy codes for correcting multiple short-duplication and edit errors. IEEE Trans. Inform. Theory 69(5), 2940–2954 (2023) Jain et al. [2017] Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Jain, S., Farnoud, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inform. Theory 63(10), 6129–6138 (2017) Elishco et al. [2019] Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Elishco, O., Farnoud, F., Schwartz, M., Bruck, J.: The entropy rate of some Pólya string models. IEEE Trans. Inform. Theory 65(12), 8180–8193 (2019) Farnoud et al. [2019] Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Farnoud, F., Schwartz, M., Bruck, J.: Estimation of duplication history under a stochastic model for tandem repeats. BMC Bioinformatics 20(64), 1–11 (2019) Elishco [2024] Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Elishco, O.: On the long-term behavior of k𝑘kitalic_k-tuples frequencies in mutation systems. arXiv preprint arXiv:2401.04020 (2024) Schoeny et al. [2017] Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Schoeny, C., Wachter-Zeh, A., Gabrys, R., Yaakobi, E.: Codes correcting a burst of deletions or insertions. IEEE Trans. Inform. Theory 63(4), 1971–1985 (2017) Bitar et al. [2021] Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Bitar, R., Hanna, S.K., Polyanskii, N., Vorobyev, I.: Optimal codes correcting localized deletions. In: Proceedings of the 2021 IEEE International Symposium on Information Theory (ISIT2021), Melbourne, Victoria, Australia, pp. 1991–1996 (2021) Wang et al. [2004] Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004) Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)
Wang, S., Tang, Y., Sima, J., Gabrys, R., Farnoud, F.: Non-binary codes for correcting a burst of at most t𝑡titalic_t deletions. IEEE Trans. Inform. Theory 70(2), 964–979 (2004)

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On the Coding Capacity of Reverse-Complement and Palindromic Duplication-Correcting Codes (2312.00394v2)

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