Construction of binary and ternary self-orthogonal linear codes

We construct new binary and ternary self-orthogonal linear codes. In order to do this we use an equivalence between the existence of a self-orthogonal linear code with a prescribed minimum distance and the existence of a solution of a certain system of Diophantine linear equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetry given by matrix groups. Using this method we found at least six new distance-optimal codes, which are all self-orthogonal.