Linear codes with few weights over finite fields

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2024-09-27 DOI:10.1016/j.ffa.2024.102509

Yan Wang , Jiayi Fan , Nian Li , Fangyuan Liu

引用次数: 0

Abstract

Linear codes with a few weights have wide applications in digital signatures, authentication codes, secret sharing protocols and some other fields. Using definition sets to construct linear codes is an effective method. In this paper, we investigate a new defining set and obtain linear codes with four weights, five weights and six weights over

F_{p}

, where p is an odd prime number. The parameters and weight distribution of the constructed linear code are completely determined by accurately calculating the exponential sum over the finite field.

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有限域上权重较少的线性编码

只有几个权重的线性编码在数字签名、验证码、秘密共享协议和其他一些领域有着广泛的应用。利用定义集来构造线性编码是一种有效的方法。本文研究了一种新的定义集，并在 Fp（其中 p 是奇素数）上获得了四重、五重和六重的线性编码。通过精确计算有限域上的指数和，可以完全确定所构建线性码的参数和权重分布。

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.

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