On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$

TL;DR

This paper investigates cyclic codes over a specific finite ring, providing generator sets and analyzing properties like rank, duality, and Hamming distance to enhance understanding of their algebraic structure.

Contribution

It introduces a generator set for cyclic codes over the ring and explores their rank, dual, and Hamming distance properties, advancing algebraic coding theory.

Findings

Derived generator sets for cyclic codes over the ring

Analyzed the rank and dual properties of these codes

Determined Hamming distance characteristics

Abstract

In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.