Minimal null designs of subspace lattice over finite fields Original Research Article

Recently, q-analogues of designs and null-designs have become interesting subjects [7–11]. However, it is not easy to construct and realize them concretely. In this paper, we characterize the minimal q-null designs for a special case. They turn out to be the signed sums of maximal isotropic subspaces of a fixed vector space, with a given bilinear form, over a finite field. Moreover, as by-products, we obtain many results on the properties of minimal q-null designs.