The [46,9,20]₂ code is unique

Titelangaben

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

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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.