Recent results and problems on constructions of linear codes from cryptographic functions

被引：41

作者：

Li, Nian ^{[1
,2
]}

Mesnager, Sihem ^{[3
,4
,5
]}

机构：

[1] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

[2] State Key Lab Cryptol, POB 5159, Beijing 100878, Peoples R China

[3] Univ Paris VIII, Dept Math, St Denis 93526, France

[4] Univ Paris XIII, Sorbonne Paris Cite 93430, LAGA, UMR 7539,CNRS, Paris, France

[5] France Telecom Paris, Palaiseau 91120, France

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2020年 / 12卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Bent function; Linear code; Perfect nonlinear function; Plateaued function; BINARY CYCLIC CODES; BENT FUNCTIONS; CROSS-CORRELATION; WEIGHT DISTRIBUTION; NONLINEAR FUNCTIONS; 3-WEIGHT CODES; FINITE-FIELDS; PERFECT; 2-WEIGHT; SEQUENCES;

D O I：

10.1007/s12095-020-00435-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Linear codes have a wide range of applications in the data storage systems, communication systems, consumer electronics products since their algebraic structure can be analyzed and they are easy to implement in hardware. How to construct linear codes with excellent properties to meet the demands of practical systems becomes a research topic, and it is an efficient way to construct linear codes from cryptographic functions. In this paper, we will introduce some methods to construct linear codes by using cryptographic functions over finite fields and present some recent results and problems in this area.

引用

页码：965 / 986

页数：22

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