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The 4-adic complexity of quaternary sequences with low autocorrelation and high linear complexity (2401.03204v1)
Published 6 Jan 2024 in cs.CR
Abstract: Recently, Jiang et al. proposed several new classes of quaternary sequences with low autocorrelation and high linear complexity by using the inverse Gray mapping (JAMC, \textbf{69} (2023): 689--706). In this paper, we estimate the 4-adic complexity of these quaternary sequences. Our results show that these sequences have large 4-adic complexity to resist the attack of the rational approximation algorithm.
- IEEE Wireless Communications, 12 (2005), 8–18.
- S. W. Golomb and G. Gong, Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar, Cambridge University Press, Cambridge, 2005.
- S. W. Golomb, Shift Register Sequences, CA:Aegean Park Press, 1967.
- M. Goresky and A. Klapper, Algebraic Shift Register Sequences, Cambridge University Press, Cambridgeshire, 2012.
- A. Klapper and M. Goresky, Feedback shift registers, 2-adic span, and combiners with memory, Journal of Cryptology, 10 (1997), 111–147.
- A. Klapper and J. Xu, Algebraic feedback shift registers, Theoretical Computer Science, 226 (1999), 61–92.
- M. Yang, S. Qiang, K. Feng and D. Lin, On the 4-adic complexity of quaternary sequences of period 2p2𝑝2p2 italic_p with ideal autocorrelation, 2021 IEEE International Symposium on Information Theory (ISIT), (2021), 1812–1816.
- M. Yang, S. Qiang, X. Jing, K. Feng and D. Lin, The 4-adic complexity of quaternary sequences of even period with ideal autocorrelation, 2022 IEEE International Symposium on Information Theory (ISIT), (2022), 528–531.
- X. Jing, Z. Xu, M. Yang and K. Feng, The 4-adic complexity of interleaved quaternary sequences of even length with optimal autocorrelation, arXiv preprint arXiv:2209.10279 (2022).
- V. Edemskiy, Symmetric 4-adic complexity of quaternary sequences with low autocorrelation and period pq𝑝𝑞pqitalic_p italic_q, Advances in Mathematics of Communications, (2023), 0–0.
- V, Edemskiy and S. Koltsova, Symmetric 4-adic complexity of quaternary sequences of length pq𝑝𝑞pqitalic_p italic_q with low autocorrelation, 2023 IEEE Information Theory Workshop (ITW), (2023), 76–80.
- V. Edemskiy and C. Wu, 4-adic complexity of quaternary cyclotomic sequences and Ding-Helleseth sequences with period pq𝑝𝑞pqitalic_p italic_q, 2022 IEEE International Symposium on Information Theory (ISIT), (2022), 372–377.
- V. Edemskiy and Z. Chen, On the 4-adic complexity of the two-prime quaternary generator, Journal of Applied Mathematics and Computing, 68 (2022), 3565–3585.
- T. Jiang and F. W. Fu, Some new classes of quaternary sequences with low autocorrelation property via two binary cyclotomic sequences, Journal of Applied Mathematics and Computing, 69 (2023), 689–706.
- Z. Yang and P. H. Ke, Quaternary sequences with odd period and low autocorrelation, Electronics letters, 46 (2010), 1–2.
- C. Zhang, X. Jing and Z. Xu, The linear complexity and 4-adic complexity of quaternary sequences with period pq𝑝𝑞pqitalic_p italic_q, Journal of Applied Mathematics and Computing, 69 (2023), 2003–2017.
- T. Cusick, C. Ding and A. Renvall, Stream ciphers and number theory, Gulf Professional Publishing, (2004).
- T. Storer, Cyclotomy and difference sets, Lectures in Advanced Mathematics, (1967).
- F. Sun, Q. Yue and X. Li, On the 2-adic complexity of cyclotomic binary sequences of order four, Applicable Algebra in Engineering, Communication and Computing, (2023), 1–19.