Let q be a prime power and F q be a finite field. In this paper, we study constacyclic codes over the ring F q + uF q + vF q + uvF q , where u 2 = u, v 2 = v and uv = vu. We characterize the generator polynomials of constacyclic codes and their duals using some decomposition of this ring. Finally we study the images of self-dual cyclic codes over F 2 m + uF 2 m + vF 2 m + uvF 2 m through a linear Gray map.

In this paper, the investigation on the algebraic structure of the ringand the description of its automorphism group, enable to study the algebraic structure of codes and their dual over this ring. We explore the algebraic structure of skew-constacyclic codes, by using a linear Gray map and we determine their generator polynomials. Necessary and sufficient conditions for the existence of self-dual skew cyclic and self-dual skew negacyclic codes over Fq[v] v q −v are given.

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.

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