English

Parameters of several families of binary duadic codes and their related codes

Information Theory 2023-02-28 v1 math.IT

Abstract

Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length 2m12^m-1 and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in \cite{LLD}. It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.

Keywords

Cite

@article{arxiv.2302.13461,
  title  = {Parameters of several families of binary duadic codes and their related codes},
  author = {Hai Liu and Chengju Li and Haifeng Qian},
  journal= {arXiv preprint arXiv:2302.13461},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2301.06446