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TITLE Linear codes from simplicial complexes
KIAS AUTHORS Hyun, Jong Yoon
JOURNAL DESIGNS CODES AND CRYPTOGRAPHY, 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.
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