Linear codes using simplicial complexes

04/18/2022

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by   Vidya Sagar, et al.

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Certain simplicial complexes are used to construct a subset D of 𝔽_2^n^m and D, in turn, defines the linear code C_D over 𝔽_2^n that consists of (v· d)_d∈ D for v∈𝔽_2^n^m. Here we deal with the case n=3, that is, when C_D is an octanary code. We establish a relation between C_D and its binary subfield code C_D^(2) with the help of a generator matrix. For a given length and dimension, a code is called distance optimal if it has the highest possible distance. With respect to the Griesmer bound, five infinite families of distance optimal codes are obtained, and sufficient conditions for certain linear codes to be minimal are established.