at Google ScholarTitle data
Kurz, Sascha:
The [46,9,20]₂ code is unique.
Bayreuth
,
2020
. - 7 p.
This is the latest version of this item.
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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: | Preprint, postprint |
|---|---|
| Keywords: | binary linear codes; optimal codes |
| Subject classification: | Mathematics Subject Classification Code: 94B05 (94B65) |
| 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 Mathematical Economics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Date Deposited: | 07 Jan 2020 07:45 |
| Last Modified: | 07 Jan 2020 07:45 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/53671 |
Available Versions of this Item
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The [46,9,20]₂ code is unique. (deposited 15 Jun 2019 21:00)
- The [46,9,20]₂ code is unique. (deposited 07 Jan 2020 07:45) [Currently Displayed]