Cyclic codes over Z(4) + uZ(4) + u(2)Z(4)

Abstract

In this paper, we study cyclic codes over the ring R = Z(4) + uZ(4) + u(2)Z(4), where u(3) = 0. We investigate Galois extensions of this ring and the ideal structure of these extensions. The results are then used to obtain facts about cyclic codes over R. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over Z(4) by considering Gray images of cyclic codes over R.