Codes from the Incidence Matrices of a zero-divisor Graphs

TL;DR

This paper explores the construction of linear codes derived from the incidence matrices of zero-divisor graphs over the ring rac{rac{Z}{n} and analyzes their main parameters.

Contribution

It introduces a method to generate linear codes from zero-divisor graphs' incidence matrices and determines their key parameters.

Findings

Main code parameters are explicitly obtained.

Codes are constructed from zero-divisor graphs over rac{rac{Z}{n}.

Provides insights into the structure of codes related to zero-divisors.

Abstract

In this paper, we examine the linear codes with respect to the Hamming metric from incidence matrices of the zero-divisor graphs with vertex set is the set of all non-zero zero-divisors of the ring $\mathbb{Z}_n$ and two distinct vertices being adjacent iff their product is zero over $\mathbb{Z}_n.$ The main parameters of the codes are obtained.