论文标题
线性互补的一对有限主理想环的组代码
Linear complementary pair of group codes over finite principal ideal rings
论文作者
论文摘要
如果$ c \ oplus d = r [g] $，a对$（c，d）组代码的组代码称为线性互补对（LCP），其中$ r $是有限的主要理想戒指，而$ g $是有限的组。我们为LCP组成的组代数（g] $，为一对$（c，d）的组代码提供了必要的条件。然后，我们证明，如果$ c $和$ d $都是$ r [g] $的组代码，那么$ c $和$ d^{\ perp} $是排列相当于的。
A pair $(C, D)$ of group codes over group algebra $R[G]$ is called a linear complementary pair (LCP) if $C \oplus D =R[G]$, where $R$ is a finite principal ideal ring, and $G$ is a finite group. We provide a necessary and sufficient condition for a pair $(C, D)$ of group codes over group algebra $R[G]$ to be LCP. Then we prove that if $C$ and $D$ are both group codes over $R[G]$, then $C$ and $D^{\perp}$ are permutation equivalent.
