at Google ScholarTitle data
Kurz, Sascha:
The [46,9,20]₂ code is unique.
In: Advances in Mathematics of Communications.
Vol. 15
(2021)
Issue 3
.
- pp. 415-422.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2020074
Official URL: 
Abstract in another language
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: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Keywords: | binary linear codes; optimal codes |
| Subject classification: | Mathematics Subject Classification Code: 94B05 (94B65) |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Date Deposited: | 08 Apr 2021 07:24 |
| Last Modified: | 15 Feb 2022 12:43 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/64619 |