Primitive Idempotents and Constacyclic Codes over Finite Chain Rings
CoRR(2019)
摘要
Let $R$ be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of $R[X]/$ where $g$ is a regular polynomial in $R[X]$. We use this set to decompose the ring $R[X]/$ and to give the structure of constacyclic codes over finite chain rings. This allows us to describe generators of the dual code $\mathcal{C}^\bot$ of a constacyclic code $\mathcal{C}$ and to characterize non-trivial self-dual constacyclic codes over finite chain rings.
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关键词
primitive idempotents,constacyclic codes,chain
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