Matrix constructions of divisible designs (Q1175275)

The authors present two new constructions for group divisible designs. One employs Kronecker products involving incidence matrices of \((v,k,\lambda)\)-designs and skew-symmetric Hadamard matrices. The other employs Kronecker products involving incidence matrices of \((v,k,\lambda)\)-designs with \(v=2k\) and adjacency matrices of strongly regular graphs in which any two distinct nonadjacent vertices have exactly one more common neighbor than do any two adjacent vertices. (Without such a restriction on strongly regular graphs, the construction yields uninteresting GDDs.) Numerous examples are provided, including several new series of divisible difference sets.