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q-analogs of designs : Subspace designs

Titelangaben

Braun, Michael ; Kiermaier, Michael ; Wassermann, Alfred:
q-analogs of designs : Subspace designs.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; Vázquez-Castro, María Ángeles (Hrsg.): Network Coding and Subspace Designs. - Cham : Springer , 2018 . - S. 171-211 . - (Signals and Communication Theory )
ISBN 978-3-319-70293-3
DOI: https://doi.org/10.1007/978-3-319-70293-3_8

Angaben zu Projekten

Projekttitel:
Offizieller ProjekttitelProjekt-ID
Random Network Coding and Designs over GF(q)IC1104

Projektfinanzierung: COST – European Cooperation in Science and Technology

Abstract

For discrete structures which are based on a finite ambient set and its subsets there exists the notion of a “q-analog”: 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 q-analogs 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, q-Steiner 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.

Weitere Angaben

Publikationsform: Aufsatz in einem Buch
Begutachteter Beitrag: Ja
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra)
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik und ihre Didaktik
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 21 Jun 2018 05:36
Letzte Änderung: 21 Jun 2018 05:36
URI: https://eref.uni-bayreuth.de/id/eprint/44594