Properties and parameters of codes from line graphs of circulant graphs

Abstract

Linear codes from neighborhood designs of strongly regular graphs such as triangular, lattice, and Paley graphs have been extensively studied over the past decade. Most of these families of graphs are line graphs of a much larger class known as circulant graphs, \( \Gamma_n(S) \). In this article, we extend earlier results to obtain properties and parameters of binary codes \( C_n(S) \) from neighborhood designs of line graphs of circulant graphs.