The study of perfect codes within Cayley graphs thus bridges abstract algebra, combinatorics, and information theory, revealing insights into symmetry, network reliability, and efficient data ...

The study of perfect codes within Cayley graphs thus bridges abstract algebra, combinatorics, and information theory, revealing insights into symmetry, network reliability, and efficient data ...

This repository provides partial datasets and the automated code for generating graph problem instances as described in the paper "GTA: Graph Theory Agent and Benchmark for Algorithmic Graph Reasoning ...

This paper develops a fundamental theory of realizations of linear and group codes on general graphs using elementary group theory, including basic group duality theory. Principal new and extended ...

In this paper, a new type of edge coloring of graphs together with an algorithm for such an edge coloring is presented to construct some column-weight three low-density parity-check (LDPC) codes whose ...