Primitive Idempotents and Constacyclic Codes over Finite Chain Rings

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