CONSTRUCTIONS OF GROUP DIVISIBLE DESIGNS

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...

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...

Construction of Group Divisible Designs

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.

Constructions of optimal quaternary constant weight codes via group divisible designs

Generalized Steiner systems GS(2, k, v, g) were first introduced by Etzion and used to construct optimal constant weight codes over an alphabet of size g + 1 with minimum Hamming distance 2k − 3, in which each codeword has length v and weight k. As to the existence of a GS(2, k, v, g), a lot of work has been done for k = 3, while not so much is known for k = 4. The notion k-GDD was first introd...