Relative projective group codes over chain rings

arXiv (Cornell University)

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.

Authors 2

1. Simon Eisenbarth Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Sihuang Hu

   Shandong University

   Affiliation as printed

   Shandong University