in the repository
Title data
Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth
,
2016
. - 21 S.
![[thumbnail of partial_spreads_and_vsp_arxiv.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
|
||||||||
|
Download (450kB)
|
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
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 |
Available Versions of this Item
- Partial spreads and vector space partitions. (deposited 21 Nov 2016 10:27) [Currently Displayed]
Download Statistics