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Designs, Codes and Cryptography
Erschienen in: Designs, Codes and Cryptography 8/2021

07.06.2021

Binary linear codes with few weights from Boolean functions

verfasst von: Xiaoqiang Wang, Dabin Zheng, Yan Zhang

Erschienen in: Designs, Codes and Cryptography | Ausgabe 8/2021

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Abstract

Boolean functions have very nice applications in coding theory and cryptography. In coding theory, Boolean functions have been used to construct linear codes in different ways. The objective of this paper is to construct binary linear codes with few weights using the defining-set approach. The defining sets of the codes presented in this paper are defined by some special Boolean functions and some additional restrictions. First, two families of binary linear codes with at most three or four weights from Boolean functions with at most three Walsh transform values are constructed and the parameters of their duals are also determined. Then several classes of binary linear codes with explicit weight enumerators are produced. Some of the binary linear codes are optimal or almost optimal according to the tables of best codes known maintained at http://​www.​codetables.​de, and the duals of some of them are distance-optimal with respect to the sphere packing bound.
Vorheriger Artikel A family of projective two-weight linear codes
Nächster Artikel Correction to: Good polynomials for optimal LRC of low locality
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Metadaten
Titel
Binary linear codes with few weights from Boolean functions
verfasst von
Xiaoqiang Wang
Dabin Zheng
Yan Zhang
Publikationsdatum
07.06.2021
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 8/2021
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-00898-0

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