The [46,9,20]_2 code is unique

06/06/2019

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by   Sascha Kurz, et al.

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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.