## Title data

Feulner, Thomas:

**Classification and nonexistence results for linear codes with prescribed minimum distances.**

*In:* Designs, Codes and Cryptography.
Vol. 70
(2014)
Issue 1-2
.
- pp. 127-138.

ISSN 1573-7586

DOI: https://doi.org/10.1007/s10623-012-9700-8

## Project information

Project title: |
Project's official title Project's id No information WA 1666/7-1 |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

Starting from a linear [n,k,d]_q code with dual distance d⊥, we may construct an [n−d⊥, k−d⊥+1, ≥d]_q code with dual distance at least ceil(d⊥/q) using construction Y1. The inverse construction gives a rule for the classification of all [n,k,d]_q codes with dual distance d⊥ by adding d⊥ further columns to the parity check matrices of the smaller codes. Isomorph rejection is applied to guarantee a small search space for this iterative approach. Performing a complete search based on this observation, we are able to prove the nonexistence of linear codes for 16 open parameter sets [n,k,d]_q , q = 2, 3, 4, 5, 7, 8. These results imply 217 new upper bounds in the known tables for the minimum distance of linear codes and establish the exact value in 109 cases.

## Further data

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

Refereed: | Yes |

Keywords: | Classification; Code equivalence; Construction Y1; Linear code; Residual code; Semilinear isometry |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) 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: | 500 Science > 510 Mathematics |

Date Deposited: | 22 Jan 2015 10:20 |

Last Modified: | 23 Nov 2022 07:52 |

URI: | https://eref.uni-bayreuth.de/id/eprint/5856 |