Double circulant codes from two class association schemes

Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and Gaborit Quadratic Double Circulant codes (QDC). As new examples SRG’s give 9 (resp. 29) new Type I (resp. Type II) [72, 36, 12] codes. We construct a [200, 100, 12] Type II code invariant under the Higman-Sims group, a [200, 100, 16] Type II code invariant under the Hall-Janko group, and more generally self-dual binary codes attached to rank three groups.