Matrix constructions of divisible designs

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 parameter...

New constructions of divisible designs

261 Davis, J.A., New constructions of divisible designs, Discrete Mathematics 120 (1993) 261-268. A construction is given for a (p2"(p+l),p,p2"+ 1(p+l),p2"+ ,p"(p+l)) (pa prime) divisible difference set in the group H x z~.+, where His any abelian group of order p+ 1. This can be used to generate a symmetric semi-regular divisible design; this is a new set of parameters for .l. 1 ;<'0, and thos...

Some constructions of divisible designs from Laguerre geometries

In the nineties, A.G. Spera introduced a construction principle for divisible designs. Using this method, we get series of divisible designs from finite Laguerre geometries. We show a close connection between some of these divisible designs and divisible designs whose construction was based on a conic in a plane of a 3-dimensional projective space.

Lifting of divisible designs

The aim of this paper is to present a construction of t-divisible designs for t > 3, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties are employed. More precisely, in a first step an abstract construction, called t-lifting, is developed. It starts from a set X containing a tdivisible design and...

Construction of Group Divisible Designs