Title data
Wassermann, Alfred ; Buratti, Marco ; Kurz, Sascha ; Nakić, Anamari ; Kiermaier, Michael:
qanalogs of group divisible designs.
2018
Event: Discretaly: A Workshop in Discrete Mathematics
, 1.2.2.2018
, Rome, Italy.
(Conference item: Workshop
,
Speech
)
Related URLs
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
Group divsible designs are wellstudied combinatorial objects. In this talk, we introduce qanalogs of group divisible designs (qGDDs). To this end, let K and G be sets of positive integers and let λ be a positive integer. The qanalog 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 2dimensional subspace of V occurs in exactly λ blocks or one group, but not both, and
3. #G > 1.
A qGDD is guniform, if all groups have the same dimension g.
We give necessary conditions on the parameters for the existence of qGDDs. Interestingly enough, one of these restrictions is connected to the existence of q^rdivisible linear codes. We also present a list of uniform qGDDs for K = {k} which we constructed with the KramerMesner method.
Further data
Item Type:  Conference item (Speech) 

Refereed:  No 
Additional notes:  Speaker: Alfred Wassermann 
Keywords:  designs; codes; divisiblecodes; 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.unibayreuth.de/id/eprint/42312 