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q-analogs of group divisible designs

URN to cite this document: urn:nbn:de:bvb:703-epub-4288-0

Title data

Buratti, Marco ; Kiermaier, Michael ; Kurz, Sascha ; Nakić, Anamari ; Wassermann, Alfred:
q-analogs of group divisible designs.
Bayreuth , 2019 . - 18 S.

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Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieNo information

Project financing: 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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): typos corrected
Keywords: group divisible designs; q-analogs; scattered subspaces; packing designs; divisible sets; Steiner systems
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Faculties
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-4288-0
Date Deposited: 12 Mar 2019 15:34
Last Modified: 14 Mar 2019 13:10
URI: https://epub.uni-bayreuth.de/id/eprint/4288

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