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 less than or equal to 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.
codes t-design harmonic weight enumerator shadow