A construction of binary linear codes from Boolean functions

被引：116

作者：

Ding, Cunsheng ^{[1
]}

机构：

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

来源：

DISCRETE MATHEMATICS | 2016年 / 339卷 / 09期

关键词：

Almost bent functions; Bent functions; Difference sets; Linear codes; Semibent functions; O-polynomials; CROSS-CORRELATION FUNCTIONS; SEMI-BENT FUNCTIONS; DESARGUESIAN PLANES; CYCLIC CODES; M-SEQUENCES; DISTRIBUTIONS; SUBCODES; WEIGHTS; OVALS; PROOF;

D O I：

10.1016/j.disc.2016.03.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed Muller codes and Kerdock codes. In the past two decades, a lot of progress on the study of applications of Boolean functions in coding theory has been made. Two generic constructions of binary linear codes with Boolean functions have been well investigated in the literature. The objective of this paper is twofold. The first is to provide a survey on recent results, and the other is to propose open problems on one of the two generic constructions of binary linear codes with Boolean functions. These open problems are expected to stimulate further research on binary linear codes from Boolean functions. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：2288 / 2303

页数：16

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