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Title data
Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth
,
2020
. - 17 S.
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Project information
| Project title: |
Project's official title Project's id Integer Linear Programming Models for Subspace Codes and Finite Geometry No information |
|---|---|
| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
In this article, the effective lengths of all q^r-divisible linear codes over GF(q) with a non-negative integer r are determined. For that purpose, the S_q(r)-adic expansion of an integer n is introduced. It is shown that there exists a q^r-divisible GF(q)-linear code of effective length n if and only if the leading coefficient of the S_q(r)-adic expansion of n is non-negative. Furthermore, the maximum weight of a q^r-divisible code of effective length n is at most the cross-sum of the S_q(r)-adic expansion of n. This result has applications in Galois geometries. A recent theorem of Nastase and Sissokho on the maximum size of a partial spread follows as a corollary. Furthermore, we get an improvement of the Johnson bound for constant dimension subspace codes.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | divisible codes; constant dimension codes; partial spreads |
| Subject classification: | Mathematics Subject Classification Code: 51E23 (05B40) |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science 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 |
| Language: | English |
| Originates at UBT: | No |
| URN: | urn:nbn:de:bvb:703-epub-4602-6 |
| Date Deposited: | 31 Jan 2020 10:45 |
| Last Modified: | 31 Jan 2020 10:47 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/4602 |
Available Versions of this Item
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On the lengths of divisible codes. (deposited 03 Apr 2019 12:22)
- On the lengths of divisible codes. (deposited 31 Jan 2020 10:45) [Currently Displayed]
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