Some optimal codes and strongly regular graphs from the linear group L 4(3) - Crnković, Dean,; Crnković, Vedrana Mikulić,; Rodrigues B.G., (Utilitas Mathematica, 2012)
We construct self-orthogonal codes obtained from the row span over F 2 or F3 of the incidence (resp. adjacency) matrices of some selforthogonal designs (resp. strongly regular graphs) defined by the action of the simple linear group L4(3) on the conjugacy classes of several of its maximal subgroups. We use the geometry of the designs or graphs and give an account on the codewords of several weights. Further, we show that the codes with parameters [27, 23, 3)3, [27, 4, 18]3, [27, 17, 6]3, [40, 29, 6]3, [117, 91, 6]2, [117, 97, 6]3, and [130, 111, 4]3 are all optimal. In addition, we obtain a self-dual [80, 40, 12] code invariant under L4(3).