Linear Codes With Two or Three Weights From Weakly Regular Bent Functions

被引：141

作者：

Tang, Chunming ^{[1
]}

Li, Nian ^{[2
]}

Qi, Yanfeng ^{[3
]}

Zhou, Zhengchun ^{[4
]}

Helleseth, Tor ^{[2
]}

机构：

[1] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Peoples R China

[2] Univ Bergen, Dept Informat, N-5020 Bergen, Norway

[3] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China

[4] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2016年 / 62卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Linear codes; weight distribution; weakly regular bent functions; cyclotomic fields; secret sharing schemes; SECRET SHARING SCHEMES; FINITE-FIELDS; NONLINEAR MAPPINGS; 3-WEIGHT CODES;

D O I：

10.1109/TIT.2016.2518678

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Linear codes with a few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. and Zhou et al. to general weakly regular bent functions and determines the weight distributions of these linear codes. It solves an open problem proposed by Ding et al. Furthermore, this paper constructs new linear codes with two or three weights and presents their weight distributions. They contain some optimal codes meeting certain bound on linear codes.

引用

页码：1166 / 1176

页数：11

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