On binary linear codes supporting t-designs

In this paper, we present classification results on self-orthogonal binary codes supporting designs, Therefore, we use special linear forms on the intersection numbers. In particular, one shows that a binary self-orthogonal code of distance d/spl les/18 whose set of minimal-weight codewords supports a 5-design has to be self-dual. We also prove that the codewords of any fixed weight in a [24m+22, 12m+11, 4m+6] Type I code support a 3-design.