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q-analogs of group divisible designs

Title data

Wassermann, Alfred ; Buratti, Marco ; Kurz, Sascha ; Nakić, Anamari ; Kiermaier, Michael:
q-analogs of group divisible designs.
2018
Event: Discretaly: A Workshop in Discrete Mathematics , 1.-2.2.2018 , Rome, Italy.
(Conference item: Workshop , Speech )

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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 in another language

Group divsible designs are well-studied combinatorial objects. In this talk, we introduce q-analogs of group divisible designs (q-GDDs). To this end, let K and G be sets of positive integers and let λ be a positive integer. The q-analog of a group divisible design of index λ and order v is a triple (V, G, B), where V is a vector space over GF(q) of dimension v, G is a vector space partition of V into subspaces (groups) whose dimensions lie in G, and B is a family of subspaces (blocks) of V that satisfy
1. if B ∈ B then dim B ∈ K,
2. every 2-dimensional subspace of V occurs in exactly λ blocks or one group, but not both, and
3. #G > 1.
A q-GDD is g-uniform, if all groups have the same dimension g.

We give necessary conditions on the parameters for the existence of q-GDDs. Interestingly enough, one of these restrictions is connected to the existence of q^r-divisible linear codes. We also present a list of uniform q-GDDs for K = {k} which we constructed with the Kramer-Mesner method.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: Speaker: Alfred Wassermann
Keywords: designs; codes; divisible-codes; group divsible designs
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: 20 Feb 2018 10:05
Last Modified: 03 May 2018 06:19
URI: https://eref.uni-bayreuth.de/id/eprint/42312