Four families of q-ary self-orthogonal codes via the defining-set construction

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-02-13 DOI:10.1016/j.ffa.2025.102586

Jiayuan Zhang, Xiaoshan Kai, Ping Li, Shixin Zhu

引用次数: 0

Abstract

Self-orthogonal codes have a wide range of applications in various fields, especially communication and cryptography. In this paper, we construct four families of linear codes over finite fields via a defining-set construction. The weight distributions of these codes are determined. We show that most of these codes are self-orthogonal and reach the Grismer bound.

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通过定义集构造得到四族q元自正交码

自正交码在通信和密码学等领域有着广泛的应用。本文通过定义集构造构造了有限域上的四族线性码。确定了这些代码的权重分布。我们证明了大多数这些码是自正交的，并且达到Grismer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.