Left Dihedral Codes over Finite Chain Rings
| Autor: | H. Aghili, R. Sobhani |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Popis: | 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 $R=\F_{p^m}$ is a Galois field, we give a classification for left $D_{2N}$-codes over $\F_{p^m}$, for any positive integer $N$. In both cases we determine dual codes and identify self-dual ones. 22 pages, submitted to Discrete Mathematics journal on 15 may 2021 |
| Databáze: | OpenAIRE |
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