论文标题
链环相对的投影组代码
Relative projective group codes over chain rings
论文作者
论文摘要
给出了$ g $的子组$ \ lbrace 1 \ rbrace $的相对投影的结构定理。因此，我们表明，固定组代数$ rg $中的所有相对投影组代码都在培养到集体代数$ \ ell $的固定链中的$ \ mathbb {f} g $，其中$ \ mathbb {f} $是$ r $ $ r $的残基领域。我们使用给定的链条以$ RG $构建双代码，并得出最小的锤重量以及最小欧几里得重量的下限。
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.
