Some optimal codes and strongly regular graphs from the linear group L4(3)

We construct self-orthogonal codes obtained from the row span over F-2 or F-3 of the incidence (resp. adjacency) matrices of some self-orthogonal designs (resp. strongly regular graphs) defined by the action of the simple linear group L-4(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 L-4(3).