Codes from Embeddings of the Strong Product of Triangular Graphs and K and Certain Induced Subgraphs

Abstract

We introduce vertex-transitive graphs \(\Gamma_n\), that are also embeddings of the strong product of triangular graphs \(L(K_n)\) and the complete graph \(K_2\). For any prime \(p\), linear codes obtained from the row span of incidence matrices of the graphs over \(\mathbb{F}_p\), are considered; their main parameters (length, dimension and minimum distance) and automorphism groups are determined. Unlike most codes that have been obtained from incidence and adjacency matrices of regular graphs by others, binary codes from the row span of incidence matrices of \(\Gamma_n\) have other minimum words apart from the rows of the matrices. Using a specific information set, PD-sets for full permutation decoding of the codes are exhibited.