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The [46,9,20]₂ code is unique

Title data

Kurz, Sascha:
The [46,9,20]₂ code is unique.
Bayreuth , 2020 . - 7 p.

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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: 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

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