## Title data

Kurz, Sascha:

**The [46,9,20]₂ code is unique.**

*In:* Advances in Mathematics of Communications.
Vol. 15
(2021)
Issue 3
.
- pp. 415-422.

ISSN 1930-5346

DOI: https://doi.org/10.3934/amc.2020074

## Abstract in another language

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.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | binary linear codes; optimal codes |

Subject classification: | Mathematics Subject Classification Code: 94B05 (94B65) |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 08 Apr 2021 07:24 |

Last Modified: | 15 Feb 2022 12:43 |

URI: | https://eref.uni-bayreuth.de/id/eprint/64619 |