Linear codes with few weights over finite fields

被引：0

作者：

Wang, Yan ^{[1
]}

Fan, Jiayi ^{[1
]}

Li, Nian ^{[2
]}

Liu, Fangyuan ^{[1
]}

机构：

[1] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Shaanxi, Peoples R China

[2] Hubei Univ, Sch Cyber Sci & Technol, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2024年 / 100卷

基金：

中国国家自然科学基金;

关键词：

Linear code; Weight distribution; Exponential sum; Finite fields; GENERIC CONSTRUCTION; 3-WEIGHT CODES; CYCLIC CODES; 2-WEIGHT; DISTRIBUTIONS; ENUMERATORS;

D O I：

10.1016/j.ffa.2024.102509

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, p , where pis 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. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：29

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