Matrix constructions of family (A) group divisible designs

In this note we use matrices to construct group divisible designs (GDDs). The constructions of GDDs of the form A 0 D + A ® D will be carried out in two cases. The first case uses the incidence matrix D of a GDD with a certain (0,1) matrix A. The second case uses the incidence matrix D of a BIBD with A as in the first case. In both cases necessary and sufficient conditions in terms of parameters of A and D are derived for N to be the incidence matrix of a GDD. This construction yields besides regular also semi-regular and singular family(A) GDDs. Moreover, this construction produces also some known GDDs constructed earlier by several authors.