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The [46,9,20]₂ code is unique

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.

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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 Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - 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

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