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Partial Spreads and Vector Space Partitions

Title data

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial Spreads and Vector Space Partitions.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; Vázquez-Castro, María Ángeles (ed.): Network Coding and Subspace Designs. - Cham : Springer , 2018 . - pp. 131-170 . - (Signals and Communication Technology )
ISBN 978-3-319-70292-6
DOI: https://doi.org/10.1007/978-3-319-70293-3_7

Official URL: Volltext

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 with the maximum possible minimum distance have been studied under the name of partial spreads in Finite Geometry for several decades. Not surprisingly, for this subclass typically the sharpest bounds on the maximal code size are known. The seminal works of Beutelspacher and Drake & Freeman on partial spreads date back to 1975 and 1979, respectively. From then until recently, there was almost no progress besides some computer-based constructions and classifications. It turns out that vector space partitions provide the appropriate theoretical framework and can be used to improve the long-standing bounds in quite a few cases. Here, we provide a historic account on partial spreads and an interpretation of the classical results from a modern perspective. To this end, we introduce all required methods from the theory of vector space partitions and Finite Geometry in a tutorial style. We guide the reader to the current frontiers of research in that field, including a detailed description of the recent improvements.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: constant dimension codes; partial spreads; vector space partitions; network coding; linear programming bound
Subject classification: Mathematics Subject Classification Code: 51E23 05B15 (05B40 11T71 94B25)
Institutions of the University: Faculties
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 in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 01 Feb 2018 07:28
Last Modified: 02 Jul 2018 08:55
URI: https://eref.uni-bayreuth.de/id/eprint/42176