WEIGHT DISTRIBUTIONS AND WEIGHT HIERARCHIES OF A CLASS OF BINARY LINEAR CODES WITH A FEW WEIGHTS

被引：0

作者：

Qiao, Xingbin ^{[1
]}

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

机构：

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

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

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

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2025年 / 19卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Binary linear code; weight distribution; weight hierarchy; generalized Hamming weight; exponential sum; GENERALIZED HAMMING WEIGHTS; 3-WEIGHT CODES; CYCLIC CODES; 2-WEIGHT;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Linear codes can be applied in consumer electronic, communication and data storage system. In addition, the weight distribution and weight hierarchy of a linear code are two significant research topics in coding theory. In this paper, by extending Li et al.'s construction in [Finite Fields Appl. 73(2021), 101865], a class of binary linear codes with a few weights is constructed by selecting the defining set properly, then the weight distributions and weight hierarchies are determined by calculating the corresponding exponential sums. In particular, the codes constructed in this paper are m-MDS codes and minimal and thus can be used in secret sharing schemes.

引用

页码：245 / 258

页数：14

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