An Analysis of Fundamental Parameters of Graph-Based Linear Error-Correcting Codes

Abstract

In this work, we develop the linear codes generated by the incidence matrices of certain finite graphs over the finite field. The main objective is to determine the fundamental parameters of the associated codes, namely the length, dimension, and minimum distance, and to examine the influence of graph structures on the resulting coding properties. Both bipartite and non-bipartite graphs are considered in this work. For the bipartite case, the Hypercube graph, Gray graph, and Nauru graph are examined, and the corresponding linear codes are shown to have parameters  respectively. Further, for the non-bipartite graphs and the Wagner graph, the associated linear codes are determined to have parameters , respectively.