A note on constacyclic codes over the ring z_3[u, v]/<u^2 −u, v^2, uv, vu>

Abstract

In this paper, we study λ-constacyclic codes over the ring R = Z₃[u, v]/<u² − u, v², uv, vu> for λ = (1 + u),(2 + 2u) and 2. We introduce a Gray map from R to Z₃³ and show that the Gray image of a cyclic code is a quasi-cyclic code of index 3. It is proved that the Gray image of λ-constacyclic code over R is permutation equivalent to either quasi-cyclic or quasi-twisted code according to the value of λ. Moreover, we determine the structure of (1+u)-constacyclic codes for an odd length n over R and give some suitable examples.