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The [46,9,20]₂ code is unique

Title data

Kurz, Sascha:
The [46,9,20]₂ code is unique.
In: Advances in Mathematics of Communications. Vol. 15 (August 2021) Issue 3 . - pp. 415-422.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2020074

Official URL: Volltext

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
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: 08 Apr 2021 07:24
URI: https://eref.uni-bayreuth.de/id/eprint/64619