The ${[46,9,20]_2}$ code is unique
Combinatorics
2020-04-15 v2 Information Theory
math.IT
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 with known bounds . Here we present a 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 and codes.
Keywords
Cite
@article{arxiv.1906.02621,
title = {The ${[46,9,20]_2}$ code is unique},
author = {Sascha Kurz},
journal= {arXiv preprint arXiv:1906.02621},
year = {2020}
}
Comments
7 pages, 3 tables, typos corrected