New Z4 codes from constacyclic codes over a non-chain ring

Let Z4 be the ring of integers modulo 4. This paper presents (1+2u+2v+2uv)-constacyclic and skew (1+2u+2v+2uv)-constacyclic codes over the ring Z4+uZ4+vZ4+uvZ4 where u2=u,v2=v,uv=vu. We define three Gray maps and show that the Gray images of (1+2u+2v+2uv)-constacyclic and skew (1+2u+2v+2uv)-constacyclic codes are cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over Z4. Also, we show that cyclic and (1+2u+2v+2uv)-constacyclic codes of odd length are principally generated. As an application, several new quaternary linear codes from the Gray images of (1+2u+2v+2uv)-constacyclic codes are obtained.