# Isodual and Self-dual Codes from Graphs

## TL;DR

This paper explores the construction of binary linear codes from graphs, providing conditions for self-duality and analyzing their minimum distance through graph theory.

## Contribution

It introduces graph-theoretic conditions for self-dual codes and offers a combinatorial interpretation of their minimum distance.

## Key findings

- Graph-based construction of binary codes
- Conditions for Type I and II self-duality
- Examples from well-known graph classes

## Abstract

Binary linear codes are constructed from graphs, in particular, by the generator matrix $[I_n|A]$ where $A$ is the adjacency matrix of a graph on $n$ vertices. A combinatorial interpretation of the minimum distance of such codes is given. We also present graph theoretic conditions for such linear codes to be Type I and Type II self-dual. Several examples of binary linear codes produced by well-known graph classes are given.