A note on cyclic codes over ℤ4 + uℤ4

In this paper, we have studied cyclic codes over the ring R = ℤ4 + uℤ4, u2 = 0. We have provided the general form of the generators of a cyclic code over R and obtained a minimal spanning set for such codes and determined their ranks. We have determined a necessary condition and a sufficient condition for cyclic codes over R to be R-free. For n = 2k, we have shown that R[x] 〈xn−1〉 is a local ring, and the complete ideal structure of R[x] 〈xn−1〉 is determined. Some examples are presented.