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arXiv · 1906.02621

The ${[46,9,20]_2}$ code is unique

Sascha Kurz
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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 $19\le d\le 20$. 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.

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Sascha Kurz. 2020-01-06. The ${[46,9,20]_2}$ code is unique. https://doi.org/10.3934/amc.2020074

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