A tighter bound on the minimum distances for an infinite family of binary BCH codes and its generalization

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-05-08 DOI:10.1016/j.ffa.2025.102628

Haodong Lu, Xuan Wang, Minjia Shi

引用次数: 0

Abstract

In this paper, we improve the bound on the minimum distance for the family of binary cyclic codes proposed by Sun et al. (2024) [8]. The 3-ary analogue is also studied in this paper, which is a nice family of ternary cyclic codes that contains some best known linear codes, and this family has a better lower bound on minimum distance than that of codes proposed by Chen et al. (2023) [2].

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无限族二进制BCH码的最小距离的更紧界及其推广

本文改进了Sun et al.(2024)[8]提出的二进制循环码族的最小距离界。本文还研究了3元模拟，这是一个很好的三元循环码族，它包含了一些最著名的线性码，并且与Chen et al.(2023)[2]提出的码相比，该族具有更好的最小距离下界。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.