The [46,9,20]2 code is unique

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.

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