Two families of negacyclic BCH codes

Xiaoqiang Wang; Zhonghua Sun; Cunsheng Ding

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arXiv · 2207.01877

Two families of negacyclic BCH codes

Xiaoqiang Wang·Zhonghua Sun·Cunsheng Ding

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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 $q$ be an odd prime power and $m$ be a positive integer. The objective of this paper is to study negacyclic BCH codes with length $\frac{q^m-1}{2}$ and $\frac{q^m+1}{2}$ over the finite field $\mathbf(q)$ 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 $q$ and $m$, 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.

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Xiaoqiang Wang, Zhonghua Sun, Cunsheng Ding. 2022-07-05. Two families of negacyclic BCH codes. https://arxiv.org/abs/2207.01877

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