Primitive Idempotents and Constacyclic Codes over Finite Chain Rings

08/16/2019

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by   Mohammed Elhassani Charkani, et al.

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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 C^ of a constacyclic code C and to characterize non-trivial self-dual constacyclic codes over finite chain rings.