Explicit efficient binary construction below the five-coefficient benchmark

Construct, for each fixed even k\geq2 and uniformly in n, an explicit family of binary codes correcting at most two unrestricted sequential palindromic duplications of length k, with polynomial-time selection of all defining parameters, polynomial-time message encoding and codeword decoding, and redundancy whose leading \log_2 n coefficient is below 5; ideally attain redundancy 2\log_2 n+O_k(\log\log n) or 2\log_2 n+O_k(1).

Background

The paper's coefficient-4 existence bound is nonconstructive and does not provide a structured encoder or decoder. A cited syndrome-parameterized construction for the stronger channel of two arbitrary insertion bursts has leading redundancy coefficient 5 and requires a suitable syndrome tuple as nonuniform advice; the paper does not assert an efficient method for selecting that tuple or a polynomial-time message encoder.

The open problem therefore seeks a uniform, explicit construction for the narrower palindromic-duplication channel, with efficient parameter selection, encoding, and decoding, and with a leading coefficient strictly below 5. For even k, any such palindromic construction would transfer to reverse-complement duplication through the alternating-complement bijection A_n.