On cyclic self-orthogonal codes over Zpm

TL;DR

This paper investigates the structure and existence conditions of cyclic self-orthogonal codes over the ring rac{p^m}{Z} and provides formulas for counting such codes of a given length.

Contribution

It derives the generator polynomial and necessary and sufficient conditions for the existence of non-trivial cyclic self-orthogonal codes over rac{p^m}{Z} and counts their number for coprime parameters.

Findings

Provides the generator polynomial for cyclic self-orthogonal codes over rac{p^m}{Z}

Establishes necessary and sufficient conditions for code existence

Counts the number of such codes of length n

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 $.