Construction of a class of at most three-weight linear codes and the applications

被引：1

作者：

Liu, Wenhui ^{[1
]}

Du, Xiaoni ^{[1
,2
,3
]}

Qiao, Xingbin ^{[1
]}

机构：

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China

[2] Northwest Normal Univ, Key Lab Cryptog & Data Analyt, Lanzhou 730070, Peoples R China

[3] Gansu Prov Res Ctr Basic Disciplines Math & Stat, Lanzhou 730070, Peoples R China

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2025年 / 36卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Linear code; Defining set; Exponential sum; Weight distribution; Secret sharing scheme; Strongly regular graph; 2-WEIGHT; SCHEMES;

D O I：

10.1007/s00200-023-00638-y

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Linear codes are widely studied due to their important applications in authentication codes, association schemes and strongly regular graphs, etc. In this paper, a class of at most three-weight linear codes is constructed by selecting a new defining set, then the parameters and weight distributions of codes are determined by exponential sums. Results show that almost all the linear codes we constructed are minimal and we also describe the access structures of the secret sharing schemes based on their dual. Especially, the new binary code is a two-weight projective code and based on which a strongly regular graph with new parameters is designed.

引用

页码：769 / 782

页数：14

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