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Upper bounds for constant dimension codes

Title data

Kurz, Sascha ; Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Wassermann, Alfred:
Upper bounds for constant dimension codes.
2017
Event: Academy Contact Forum "Coding Theory and Cryptography VII" , 06.10.2017 , Brüssel, Belgien.
(Conference item: Workshop , Speech )

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

Constant dimension codes were introduced to correct errors and/or erasures over the operator channel in random network coding. More precisely, they are subsets of the set of k-dimensional subspaces of GF(q)^v such that the intersection between any two codewords has dimension at most t. Setting the minimum distance to d:= 2k-2t, i.e., the so-called subspace distance, one can ask for the maximum cardinality A_q(v;d;k) of such a code given the parameters q, v, k, and d. In this talk we will review the known upper bounds for constant dimension codes and highlight their relations. More recent upper bounds based on the linear programming method for linear (projective) divisible block codes or integer linear programming formulations will also be discussed.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: Speaker: Sascha Kurz
Keywords: network coding; subspace codes; constant dimension codes; linear programming; coding theory
Subject classification: MSC: 51E23 (05B15 05B40 11T71 94B25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 11 Oct 2017 09:27
Last Modified: 11 Oct 2017 09:27
URI: https://eref.uni-bayreuth.de/id/eprint/39972