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Applicable Algebra in Engineering, Communication and Computing
Erschienen in: Applicable Algebra in Engineering, Communication and Computing 4/2021

02.01.2020 | Original Paper

Projective binary linear codes from special Boolean functions

verfasst von: Ziling Heng, Weiqiong Wang, Yan Wang

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 4/2021

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Abstract

Linear codes with a few weights have nice applications in communication, secret sharing schemes, authentication codes, association schemes, block designs and so on. Projective binary linear codes are one of the most important subclasses of linear codes for practical applications. The objective of this paper is to construct projective binary linear codes with some special Boolean functions. Four families of binary linear codes with three or four weights are derived and the parameters of their duals are also determined. It turns out that the duals of these codes are optimal or almost optimal with respect to the sphere-packing bound. As applications, the codes presented in this paper can be used to construct association schemes and secret sharing schemes with interesting access structures.
Vorheriger Artikel Explicit maximal and minimal curves of Artin–Schreier type from quadratic forms

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Metadaten
Titel
Projective binary linear codes from special Boolean functions
verfasst von
Ziling Heng
Weiqiong Wang
Yan Wang
Publikationsdatum
02.01.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Applicable Algebra in Engineering, Communication and Computing / Ausgabe 4/2021
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-019-00412-z

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