Generalized graph codes and thier minimum distances

TL;DR

This paper extends the concept of graph codes to general l-partite graphs, providing bounds on minimum distance and examples with calculated parameters, advancing the theoretical understanding of graph-based codes.

Contribution

It introduces a generalized definition of graph codes for l-partite graphs and derives lower bounds on their minimum distances, along with illustrative examples.

Findings

Lower bound on minimum distance for generalized graph codes

Explicit example with calculated parameters [n, k, d]

Extension of graph code theory to l-partite structures

Abstract

Graph code is a linear code obtained from linear codes $C$ and a certain bipartite graph G. In this paper, I propose an expansion of the definition of graph code to general $l$-partite, and give its lower bound of minimum distance. I also give an example of generalized graph code and calculate its parameters $[n, k, d]$.