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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.

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Official URL: Volltext

Project information

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

Project financing: Deutsche Forschungsgemeinschaft

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.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Keywords: group divisible designs, q-analogs, scattered subspaces, packing designs, divisible sets, Steiner systems
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
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 05 May 2018 21:00
Last Modified: 07 May 2018 05:40
URI: https://eref.uni-bayreuth.de/id/eprint/44008

Available Versions of this Item