Relative projective group codes over chain rings

Simon Eisenbarth; Sihuang Hu

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arXiv · 2010.12429

Relative projective group codes over chain rings

Simon Eisenbarth·Sihuang Hu

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Abstract

A structure theorem of the group codes which are relative projective for the subgroup $\lbrace 1 \rbrace$ 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 $\ell$ in the group algebra $\mathbb{F}G$, where $\mathbb{F}$ 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.

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Simon Eisenbarth, Sihuang Hu. 2020-10-23. Relative projective group codes over chain rings. https://arxiv.org/abs/2010.12429

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