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Title data
Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth
,
2017
. - 30 S.
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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. 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 DOI: https://doi.org/10.1007/978-3-319-70293-3_7 |
| 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-3244-2 |
| Date Deposited: | 20 Mar 2017 09:13 |
| Last Modified: | 27 May 2021 08:42 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/3244 |
Available Versions of this Item
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Partial spreads and vector space partitions. (deposited 21 Nov 2016 10:27)
- Partial spreads and vector space partitions. (deposited 20 Mar 2017 09:13) [Currently Displayed]
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