q-analogs of group divisible designs

Title data

Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred:
q-analogs of group divisible designs.
Bayreuth , 2018 . - 17 p.

Project information

Abstract in another language

A well known class of objects in combinatorial design theory are group divisible designs.Here, we introduce the q-analogs of group divisible designs. It turns out that there are interesting connections to scattered subspaces, q-Steiner systems, design packings and $q^r$-divisible projective sets.

We give necessary conditions for the existence of q-analogs of group divisible designs, construct an infinite series of examples, and provide further existence results with the help of a computer search.

One example is a (6,3,2,2)_2 group divisible design over GF(2) which is a design packing consisting of 180 blocks that such every 2-dimensional subspace in GF(2)^6 is covered at most twice.