In this paper, we study (1 + 2u + 2v)-constacyclic and skew (1 + 2u +
2v)-constacyclic codes over the ring Z4 + uZ4 + vZ4 + uvZ4 where u2 = v2 =
0,uv = vu. We define some new Gray maps and show that the Gray images of (1
+ 2u + 2v)-constacyclic and skew (1 + 2u + 2v)-constacyclic codes are
cyclic, quasi-cyclic and permutation equivalent to quasi-cyclic codes over
Z4. Further, we determine the structure of (1 + 2u + 2v)-constacyclic codes
of odd length n.
