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URN to cite this document: urn:nbn:de:bvb:703-epub-5780-8
Title data
Kurz, Sascha:
The interplay of different metrics for the construction of constant dimension codes.
Bayreuth
,
2021
. - 18 S.
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Abstract
A basic problem for constant dimension codes is to determine the maximum possible size A<sub>q</sub>(n,d;k) of a set of k-dimensional subspaces in GF(q)<sup>n</sup>, called codewords, such that the subspace distance is at least d for all pairs of different codewords U, W. Constant dimension codes have applications in e.g. random linear network coding, cryptography, and distributed storage. Bounds for A<sub>q</sub>(n,d;k) are the topic of many recent research papers. Providing a general framework we survey many of the latest constructions and show up the potential for further improvements. As examples we give improved constructions for the cases A<sub>q</sub>(10,4;5), A<sub>q</sub>(11,4;4), A<sub>q</sub>(12,6;6), and A<sub>q</sub>(15,4;4). We also derive general upper bounds for subcodes arising in those constructions.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | Galois geometry; subspace distance; constant dimension codes; subspace codes; random linear network coding |
| Subject classification: | Mathematics Subject Classification Code: 51E23 05B40 (11T71 94B25) |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 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 Mathematical Economics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-5780-8 |
| Date Deposited: | 23 Sep 2021 09:00 |
| Last Modified: | 23 Sep 2021 09:01 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/5780 |
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