Primitive idempotents and constacyclic codes over finite chain rings

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Résumé

Let R be a commutative local nite 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
nite 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 finite chain rings.

Mots-clés

finite chain ring, idempotent, constacyclic code