Left Dihedral Codes over Finite Chain Rings
(2105.07499)Abstract
Let $R$ be a finite commutative chain ring, $D{2n}$ be the dihedral group of size $2n$ and $R[D{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D{2n}]$ (called left $D{2n}$-codes) when ${\rm gcd}(char(R),n)=1$. In this way, we explore the structure of some skew-cyclic codes of length 2 over $R$ and also over $R\times S$, where $S$ is an isomorphic copy of $R$. As a particular result, we give the structure of cyclic codes of length 2 over $R$. In the case where $R=\F{pm}$ is a Galois field, we give a classification for left $D{2N}$-codes over $\F_{pm}$, for any positive integer $N$. In both cases we determine dual codes and identify self-dual ones.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.