Linear Codes from Simplicial Complexes over $\mathbb{F}_{2^n}$

Hongwei LiuZihao Yu

Mar 2023

摘要

In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ andtheir binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtainedfrom mathematical objects called simplicial complexes. We use a result in LFSRsequences to illustrate the relation of the weights of codewords in two specialcodes obtained from simplical complexes and then determin the parameters ofthese codes. We construct fiveinfinite families of distance optimal codes andgive sufficient conditions for these codes to be minimal.

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