Publications by the same author
plus in the repository
plus in Google Scholar

Bibliografische Daten exportieren

Partial spreads and vector space partitions

URN to cite this document: urn:nbn:de:bvb:703-epub-3244-2

Title data

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth , 2017 . - 30 S.

This is the latest version of this item.

[thumbnail of extended version]
Format: PDF (extended version)
Name: partial_spreads_and_vsp_rev_arxiv.pdf
Version: Published Version
Available under License Creative Commons BY 4.0: Attribution
Download (314kB)

Project information

Project title:
Project's official title
Project's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche Geometrie
No information

Project financing: Deutsche Forschungsgemeinschaft


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: Preprint, postprint
Additional notes (visible to public): erschienen in:
Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; Vázquez-Castro, María Ángeles (Hrsg.): Network Coding and Subspace Designs. - Cham : Springer , 2018 . - S. 131-170 . - (Signals and Communication Technology )
ISBN 978-3-319-70292-6
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 > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3244-2
Date Deposited: 20 Mar 2017 09:13
Last Modified: 27 May 2021 08:42

Available Versions of this Item


Downloads per month over past year