Identifying cyclic and (1 + 2v)-constacyclic codes over Z₄[v]/ <v³ – 1> with Z₄-linear codes

This paper studies cyclic and (1 + 2v)-constacyclic codes over the ring Z₄[v]/. By introducing three different Gray maps, we show that the Gray images of cyclic codes are quasi-cyclic codes over Z₄ and that of (1 + 2v)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z₄. Moreover, we show that the Gray image of skew (1 + 2v)-constacyclic code is a quasi-cyclic code over Z₄.Publisher's Versio