Title data
Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth
,
2017
.  30 p.
This is the latest version of this item.
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 
Abstract in another language
Constantdimension 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 computerbased constructions and classifications. It turns out that vector space partitions provide the appropriate theoretical framework and can be used to improve the longstanding 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 

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 > 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 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  20 Mar 2017 09:21 
Last Modified:  18 Mar 2019 15:23 
URI:  https://eref.unibayreuth.de/id/eprint/36602 
Available Versions of this Item

Partial spreads and vector space partitions. (deposited 26 Nov 2016 22:00)
 Partial spreads and vector space partitions. (deposited 20 Mar 2017 09:21) [Currently Displayed]