Codes arising from directed strongly regular graphs with μ = 1

The rank of adjacency matrix plays an important role in construction of linear codes from a directed strongly regular graph using different techniques, namely, code orthogonality, adjacency matrix determinant and adjacency matrix spectrum. The problem of computing the dimensions of such codes is an intriguing one. Several conjectures to determine the rank of adjacency matrix of a DSRG Gamma over a finite field, keep researchers working in this area. To address the same to an extent, we have considered the problem of finding the rank over a finite field of the adjacency matrix of a DSRG G(v, k, t,lambda, mu) with mu = 1, including some mixed Moore graphs and corresponding codes arising from them, in this paper.