in the repository
URN to cite this document: urn:nbn:de:bvb:703-epub-4398-7
Title data
Kurz, Sascha:
The [46,9,20]₂ code is unique.
Bayreuth
,
2019
. - 7 S.
There is a more recent version of this item available.
![[thumbnail of 46_9_20.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
|
||||||||
|
Download (213kB)
|
Abstract
The minimum distance of all binary linear codes with dimension at most eight is known. The smallest open case for dimension nine is length n=46 with known bounds 19≤d≤20. Here we present a [46,9,20]₂ code and show its uniqueness. Interestingly enough, this unique optimal code is asymmetric, i.e., it has a trivial automorphism group. Additionally, we show the non-existence of [47,10,20]₂ and [85,9,40]₂ codes.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | binary linear codes; optimal codes |
| Subject classification: | Mathematics Subject Classification Code: 94B05 (94B65) |
| 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 > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau Faculties Faculties > Faculty of Mathematics, Physics und Computer Science |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-4398-7 |
| Date Deposited: | 11 Jun 2019 06:20 |
| Last Modified: | 11 Jun 2019 06:20 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/4398 |
Available Versions of this Item
- The [46,9,20]₂ code is unique. (deposited 11 Jun 2019 06:20) [Currently Displayed]
Download Statistics