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Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred:
q-analogs of group divisible designs.
In: Schmidt, Kai-Uwe ; Winterhof, Arne
(Hrsg.):
Combinatorics and Finite Fields : Difference Sets, Polynomials, Pseudorandomness and Applications. -
Berlin
: De Gruyter
,
2019
. - (Radon Series on Computational and Applied Mathematics
; 23
)
ISBN 978-3-11-064179-0
Angaben zu Projekten
| Projekttitel: |
Offizieller Projekttitel Projekt-ID Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie Ohne Angabe |
|---|---|
| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
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.