Title data
Kurz, Sascha:
The [46,9,20]₂ code is unique.
Bayreuth
,
2020
.  7 p.
This is the latest version of this item.
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 nonexistence 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.unibayreuth.de/id/eprint/53671 
Available Versions of this Item

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]