Some constacyclic BCH codes with good parameters

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-02 DOI:10.1007/s10623-024-01433-7

Jin Li, Huilian Zhu, Shan Huang

引用次数: 0

Abstract

BCH codes as a subclass of constacyclic BCH codes have been widely studied, while the results on the parameters of BCH codes over finite fields are still very limited. In this paper, we investigate some q-ary BCH codes and \(\lambda \)-constacyclic BCH codes of length \(q^{m}+1\), where q is a prime power and \(\textrm{ord}(\lambda )\mid q-1\). We determine the dimensions of these codes with some large designed distances, and give good lower bounds on the minimum distance. The code examples presented in this paper indicate that these codes contain many distance-optimal codes and codes with best known parameters.

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一些参数良好的常环 BCH 编码

BCH 码作为常环 BCH 码的一个子类已被广泛研究，而关于有限域上 BCH 码参数的研究结果仍然非常有限。在本文中，我们研究了长度为 \(q^{m}+1\) 的一些 qary BCH 码和（q^{m}+1\）的（\textrm{ord}(\lambda )\mid q-1\）constacyclic BCH 码，其中 q 是素幂且（\textrm{ord}(\lambda )\mid q-1\）。我们用一些大的设计距离确定了这些编码的维数，并给出了最小距离的良好下限。本文给出的编码示例表明，这些编码包含许多距离最优编码和具有已知最佳参数的编码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.