Isodual and self-dual codes from graphs

Binary linear codes are constructed from graphs, in particular, by the generator matrix $[I_n\mid A]$ where $A$ is the adjacency matrix of a graph on $n$ vertices. A combinatorial interpretation of the minimum distance of such codes is given. We also present graph theoretic conditions for such linear codes to be Type I and Type II self-dual. Several examples of binary linear codes produced by well-known graph classes are given.