Linear Codes from Simplicial Complexes over 𝔽_2^n

03/16/2023

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by   Hongwei Liu, et al.

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In this article we mainly study linear codes over 𝔽_2^n and their binary subfield codes. We construct linear codes over 𝔽_2^n whose defining sets are the certain subsets of 𝔽_2^n^m obtained from mathematical objects called simplicial complexes. We use a result in LFSR sequences to illustrate the relation of the weights of codewords in two special codes obtained from simplical complexes and then determin the parameters of these codes. We construct fiveinfinite families of distance optimal codes and give sufficient conditions for these codes to be minimal.