Title data
Braun, Michael ; Kiermaier, Michael ; Wassermann, Alfred:
qanalogs of designs : Subspace designs.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; VázquezCastro, María Ángeles
(ed.):
Network Coding and Subspace Designs. 
Cham
: Springer
,
2018
.  pp. 171211
.  (Signals and Communication Theory
)
ISBN 9783319702933
DOI: https://doi.org/10.1007/9783319702933_8
Project information
Project title: 



Project financing: 
COST – European Cooperation in Science and Technology 
Abstract in another language
For discrete structures which are based on a finite ambient set and its subsets there exists the notion of a “qanalog”: For this, the ambient set is replaced by a finite vector space and the subsets are replaced by subspaces. Consequently, cardinalities of subsets become dimensions of subspaces. Subspace designs are the qanalogs of combinatorial designs. Introduced in the 1970s, these structures gained a lot of interest recently because of their application to random network coding. In this chapter we give a thorough introduction to the subject starting from the subspace lattice and its automorphisms, the Gaussian binomial coefficient and counting arguments in the subspace lattice. This prepares us to survey the known structural and existence results about subspace designs. Further topics are the derivation of subspace designs with related parameters from known subspace designs, as well as infinite families, intersection numbers, and automorphisms of subspace designs. In addition, qSteiner systems and so called large sets of subspace designs will be covered. Finally, this survey aims to be a comprehensive source for all presently known subspace designs and large sets of subspace designs with small parameters.
Further data
Item Type:  Article in a book 

Refereed:  Yes 
Institutions of the University:  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 and Didactics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  21 Jun 2018 05:36 
Last Modified:  23 Jan 2019 10:10 
URI:  https://eref.unibayreuth.de/id/eprint/44594 