On the number of minimal codewords in codes generated by the adjacency matrix of a graph

TL;DR

This paper investigates the number of minimal codewords in binary linear codes derived from the adjacency matrix of a graph with an appended identity matrix, relevant for decoding and cryptography.

Contribution

It introduces a study of minimal codewords in codes generated by adjacency matrices with appended identity matrices, a novel approach in coding theory.

Findings

Characterizes the number of minimal codewords in these codes

Provides bounds or formulas for minimal codeword counts

Links graph properties to code minimality

Abstract

Minimal codewords have applications in decoding linear codes and in cryptography. We study the number of minimal codewords in binary linear codes that arise by appending a unit matrix to the adjacency matrix of a graph.