On cyclic self-orthogonal codes over Zpm

Abstract: 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 $.