On cyclic self-orthogonal codes over Zpm

The purpose of this paper is to study the cyclic self orthogonal codes over ${\mathbb{Z}}_{p^m}$. After providing the generator polynomial of cyclic self orthogonal codes over ${\mathbb{Z}}_{p^m}$, we give the necessary and sufficient condition for the existence of non-trivial self orthogonal codes over ${\mathbb{Z}}_{p^m}$ . We have also provided the number of such codes of length $n$ over ${\mathbb{Z}}_{p^m}$ for any $(p,n)=1$.