English

Two families of negacyclic BCH codes

Information Theory 2022-07-06 v1 math.IT

Abstract

Negacyclic BCH codes are a subclass of neagcyclic codes and are the best linear codes in many cases. However, there have been very few results on negacyclic BCH codes. Let qq be an odd prime power and mm be a positive integer. The objective of this paper is to study negacyclic BCH codes with length qm12\frac{q^m-1}{2} and qm+12\frac{q^m+1}{2} over the finite field (q)\mathbf(q) and analyse their parameters. The negacyclic BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes. For certain qq and mm, compared with cyclic codes with the same dimension and length, the negacyclic BCH codes presented in this paper have a larger minimum distance in some cases.

Keywords

Cite

@article{arxiv.2207.01877,
  title  = {Two families of negacyclic BCH codes},
  author = {Xiaoqiang Wang and Zhonghua Sun and Cunsheng Ding},
  journal= {arXiv preprint arXiv:2207.01877},
  year   = {2022}
}