On the codes over the Z_3+vZ_3+v^2Z_3

Abstract

In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R = Z3 +vZ3 +v 2 Z3, v 3 = v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasicyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error correcting codes are obtained from both cyclic and negacyclic codes over R. It is given some examples. Firstly, quasi-constacyclic and skew quasi-constacyclic codes are introduced. By giving two Hermitian product, it is investigated their duality. A sufficient condition for 1-generator skew quasiconstacyclic codes to be free is determined.