On cyclic self-orthogonal codes over Z2mZ2m

In this paper, we study cyclic self-orthogonal codes over Z2mZ2m for any odd length. We give the generator polynomials of cyclic self-orthogonal codes over Z2mZ2m. By using these generator polynomials, we obtain a sufficient and necessary condition for the existence of nontrivial cyclic self-orthogonal codes over Z2mZ2m and determine the number of such codes for a given odd length. Some results about cyclic self-dual codes over Z2mZ2m are included.