Relative projective group codes over chain rings

10/23/2020

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by   Simon Eisenbarth, et al.

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A structure theorem of the group codes which are relative projective for the subgroup { 1 } of G is given. With this, we show that all such relative projective group codes in a fixed group algebra RG are in bijection to the chains of projective group codes of length ℓ in the group algebra 𝔽G, where 𝔽 is the residue field of R. We use a given chain to construct the dual code in RG and also derive the minimum Hamming weight as well as a lower bound of the minimum euclidean weight.