Linear Codes from Incidence Matrices of Unit Graphs

TL;DR

This paper studies binary linear codes derived from the incidence matrices of unit graphs over cyclic groups, analyzing their parameters and properties within the Hamming metric framework.

Contribution

It introduces a new class of codes based on the incidence matrices of unit graphs and determines their main parameters.

Findings

Codes' parameters are explicitly computed.

The structure of the codes depends on the properties of the unit graph.

Insights into the relationship between graph structure and code properties.

Abstract

In this paper, we examine the binary linear codes with respect to Hamming metric from incidence matrix of a unit graph $G(\mathbb{Z}_{n})$ with vertex set is $\mathbb{Z}_{n}$ and two distinct vertices $x$ and $y$ being adjacent if and only if $x+y$ is unit. The main parameters of the codes are given.