Minimal Linear Codes From Characteristic Functions

被引：30

作者：

Mesnager, Sihem ^{[1
,2
,3
]}

Qi, Yanfeng ^{[4
]}

Ru, Hongming ^{[5
]}

Tang, Chunming ^{[5
,6
]}

机构：

[1] Univ Paris VIII, Dept Math, F-93526 St Denis, France

[2] Univ Sorbonne Paris Nord, Lab Geometrie Anal & Applicat, CNRS, UMR 7539,LAGA, F-93430 Villetaneuse, France

[3] Telecom Paris, F-91120 Palaiseau, France

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

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

[6] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Hong Kong, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Linear codes; Minimal linear code; characteristic function; subspace; weight distribution; CONSTRUCTION; BENT; GEOMETRY;

D O I：

10.1109/TIT.2020.2978387

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of F-q to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of F-q, we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes.

引用

页码：5404 / 5413

页数：10

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