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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 title Project's id Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie No 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 (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics 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

Available Versions of this Item

q-analogs of group divisible designs. (deposited 04 May 2018 06:21)
- q-analogs of group divisible designs. (deposited 12 Mar 2019 15:34) [Currently Displayed]

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