Several classes of linear codes with few weights derived from Weil sums

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-06-16 DOI:10.1016/j.ffa.2025.102679

Zhao Hu , Mingxiu Qiu , Nian Li , Xiaohu Tang , Liwei Wu

引用次数: 0

Abstract

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of t-weight linear codes over

F_{q}

are presented with the defining sets given by the intersection, difference and union of two certain sets, where

t = 3, 4, 5, 6

and q is an odd prime power. By using Weil sums and Gauss sums, the parameters and weight distributions of these codes are determined completely. Moreover, three classes of optimal codes meeting the Griesmer bound are obtained, and computer experiments show that many (almost) optimal codes can be derived from our constructions.

查看原文本刊更多论文

由Weil和导出的几类少权线性码

低权重的线性码在秘密共享、认证码、关联方案和强正则图中有广泛的应用。本文给出了Fq上的几类t权线性码的定义集，其中t=3、4、5、6，且q为奇素数幂。利用Weil和和和的方法，完整地确定了这些码的参数和权值分布。此外，还得到了满足Griesmer界的三类最优码，计算机实验表明，从我们的构造中可以得到许多（几乎）最优码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.