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Primitive Idempotents and Constacyclic Codes over Finite Chain Rings (1908.07368v1)
Published 16 Aug 2019 in cs.IT, math.IT, and math.RA
Abstract: Let $R$ be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of $R[X]/<g>$ where $g$ is a regular polynomial in $R[X]$. We use this set to decompose the ring $R[X]/<g>$ 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.