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Partial spreads and vector space partitions

URN to cite this document: urn:nbn:de:bvb:703-epub-3039-8

Title data

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth , 2016 . - 21 S.

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Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract

Constant dimension codes with the maximum possible minimum distance have been studied under the name of partial spreads in finite geometry for several decades. It is no surprise that the sharpest bounds on the maximal code sizes are typically known for this subclass. The seminal works of Andr\'e, Segre, Beutelspacher, and Drake & Freeman date back to 1954, 1964, 1975, and 1979, respectively. 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, Here, we provide an historic account and an interpretation of the classical results from a modern point of view. 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.

Further data

Item Type: Preprint, postprint
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)
DDC Subjects: 500 Science > 510 Mathematics
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 II (Computer Algebra)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3039-8
Date Deposited: 21 Nov 2016 10:27
Last Modified: 28 Mar 2019 10:40
URI: https://epub.uni-bayreuth.de/id/eprint/3039

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