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Linear codes from simplicial complexes

Title
Linear codes from simplicial complexes
Authors
Chang S.Hyun J.Y.
Ewha Authors
장승환
SCOPUS Author ID
장승환scopus
Issue Date
2017
Journal Title
Designs, Codes, and Cryptography
ISSN
0925-1022JCR Link
Citation
pp. 1 - 15
Keywords
Binany linear codeBoolean functionMinimal linear codeOptimal linear codeSecret sharing schemeSimplicial complexWalsh–Hadamard transform
Publisher
Springer New York LLC
Indexed
SCI; SCIE; SCOPUS scopus
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. © 2017 Springer Science+Business Media, LLC, part of Springer Nature
DOI
10.1007/s10623-017-0442-5
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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