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arXiv · 2012.13239

Linear complementary pair of group codes over finite principal ideal rings

Hualu Liu·Xiusheng Liu
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Abstract

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.

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Hualu Liu, Xiusheng Liu. 2020-12-24. Linear complementary pair of group codes over finite principal ideal rings. https://arxiv.org/abs/2012.13239

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