## Title data

Kiermaier, Michael ; Wassermann, Alfred ; Zwanzger, Johannes:

**New upper bounds on binary linear codes and a ℤ₄-code with a better-than-linear Gray image.**

*In:* IEEE Transactions on Information Theory.
Vol. 62
(2016)
Issue 12
.
- pp. 6768-6771.

ISSN 0018-9448

DOI: https://doi.org/10.1109/TIT.2016.2612654

## Project information

Project title: |
Project's official title Project's id No information WA-1666/4 |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft Studienstiftung des deutschen Volkes |

## Abstract in another language

Using integer linear programming and table-lookups, we prove that there is no binary linear [1988, 12, 992] code. As a by-product, the non-existence of binary linear codes with the parameters [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] is shown. Our work is motivated by the recent construction of the extended dualized Kerdock code K6*, which is a Z4-linear code having a non-linear binary Gray image with the parameters 1988, 212,992. By our result, the code K6* can be added to the small list of Z4-codes for which it is known that the Gray image is better than any binary linear code.

## Further data

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

Refereed: | Yes |

Keywords: | integer linear programming; linear codes; ring-linear codes; Kerdock codes |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 04 May 2017 11:11 |

Last Modified: | 02 Feb 2022 14:28 |

URI: | https://eref.uni-bayreuth.de/id/eprint/36947 |