Two-weight codes, graphs and orthogonal arrays

We investigate properties of two-weight codes over finite Frobenius rings, giving constructions for the modular case. A δ-modular code [15] is characterized as having a generator matrix where each column g appears with multiplicity δ|gR×| for some δ ∈ Q. Generalizing [10] and [5], we show that the additive group of a two-weight code satisfying certain constraint equations (and in particular a modular code) has a strongly regular Cayley graph and derive existence conditions on its parameters. We provide a construction for an infinite family of modular two-weight codes arising from unions of submodules with pairwise trivial intersection. The corresponding strongly regular graphs are isomorphic to graphs from orthogonal arrays.