A construction of binary linear codes from Boolean functions

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 theor...

Full description

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 339; no. 9; pp. 2288 - 2303
Main Author Ding, Cunsheng
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.09.2016
Subjects
Almost bent functions
Bent functions
Difference sets
Linear codes
O-polynomials
Semibent functions
Linear codes
Difference sets
Semibent functions
O-polynomials
Bent functions
Almost bent functions
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2016.03.029