q-Analoga von Designs, Subspace Codes und verwandte Objekte

Titelangaben

Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
q-Analoga von Designs, Subspace Codes und verwandte Objekte.
2018
Veranstaltung: Gemeinsame Jahrestagung GDMV 2018 , 05.-09.03.2018 , Paderborn.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

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Abstract

In the 1970s, Ray-Chaudhuri, Cameron and Delsarte independently introduced q-analogs of designs. It turns out that a subclass - namely q-analogs of Steiner systems
- are the best possible constant-dimension subspace codes for random network coding (see Kötter, Kschischang 2008). This is analog to the situation in “classical” coding
theory, where (combinatorial) Steiner systems are the best possible constant-weight codes for a given length and minimum distance. In this talk we will give an introduction to the subject and survey recent developments in q-analogs of designs and subspace codes. Further, we will point out connections to finite geometry and other areas in coding theory. For an in-depth introduction see also the forthcoming book by Greferath, M., Pavčević, M.O., Silberstein, N., Vázquez-Castro, M.Á. (Eds.): Network Coding and Subspace Designs, Springer (2018).