Cyclic and Constacyclic Codes for F<sub>2</sub>[u,v]/<u<sup>2</sup>,v<sup>3</sup> – v,uv,vu>

Abstract

In this paper, we study cyclic and β-constacyclic codes over the ?nite commutative ring R = F2[u,v]/<u2,v3 ? v,uv,vu> with ? = (1+u),(1+u+v+v2) and (1+v+v2). We establish a Gray map from R to F42 and prove that the Gray image of a cyclic code is a quasi-cyclic code of index 4. It is also shown that the Gray image of β-constacyclic code overRis either β-equivalent, β-equivalent or β-equivalent to a quasi-cyclic code of length 4n and index 4 over F2 when ? = (1 + u),(1 + u + v + v2) and (1 + v + v2), respectively.