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Designs, Codes and Cryptography

Erschienen in:

24.11.2017

Linear codes from simplicial complexes

verfasst von: Seunghwan Chang, Jong Yoon Hyun

Erschienen in: Designs, Codes and Cryptography | Ausgabe 10/2018

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Abstract

In this article we introduce a method of constructing binary linear codes and computing their weights by means of Boolean functions arising from mathematical objects called simplicial complexes. Inspired by Adamaszek (Am Math Mon 122:367–370, 2015) we introduce n-variable generating functions associated with simplicial complexes and derive explicit formulae. Applying the construction (Carlet in Finite Field Appl 13:121–135, 2007; Wadayama in Des Codes Cryptogr 23:23–33, 2001) of binary linear codes to Boolean functions arising from simplicial complexes, we obtain a class of optimal linear codes and a class of minimal linear codes.

Vorheriger Artikel A class of negacyclic BCH codes and its application to quantum codes

Nächster Artikel Some new Kirkman signal sets

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Titel: Linear codes from simplicial complexes
verfasst von: Seunghwan Chang
Jong Yoon Hyun
Publikationsdatum: 24.11.2017
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 10/2018
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0442-5

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Linear codes from simplicial complexes

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