A class of constacyclic codes and skew constacyclic codes over Z2s + uZ2s and their gray images

In this paper, we study (1+2(s-1)u)-constacyclic codes and a class of skew(1+ 2(s-1)u)-constacyclic codes of odd length over the ring R = Z(2s) + uZ(2s), u(2) = 0, where s >= 3 is an odd integer. We have obtained the algebraic structure of (1+2(s-1)u)-constacyclic codes over R. Three new Gray maps from R to Z(2) + uZ(2) have been defined and it is shown that Gray images of (1 + 2(s-1)u)-constacyclic codes and skew (1 + 2(s-1)u)-constacyclic codes are cyclic codes, quasi-cyclic codes or codes that are permutation equivalent to quasi-cyclic codes over Z(2) + uZ(2). Using Magma, some good cyclic codes of length 6 over Z(2) + uZ(2) are obtained.