## Title data

Kiermaier, Michael ; Kurz, Sascha:

**Classification of Δ-Divisible Linear Codes Spanned by Codewords of Weight Δ.**

*In:* IEEE Transactions on Information Theory.
Vol. 69
(2023)
Issue 6
.
- pp. 3544-3551.

ISSN 0018-9448

DOI: https://doi.org/10.1109/TIT.2023.3239582

## Abstract in another language

We classify all q-ary Δ-divisible linear codes which are spanned by codewords of weight Δ. The basic building blocks are the simplex codes, and for q=2 additionally the first order Reed-Muller codes and the parity check codes. This generalizes a result of Pless and Sloane, where the binary self-orthogonal codes spanned by codewords of weight 4 have been classified, which is the case q=2 and Δ=4 of our classification. As an application, we give an alternative proof of a theorem of Liu on binary Δ-divisible codes of length 4Δ in the projective case.

## Further data

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

Refereed: | Yes |

Keywords: | linear codes; divisible codes; classification |

Subject classification: | Mathematics Subject Classification Code: 94B05 |

Institutions of the University: | 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 Mathematical Economics |

Result of work at the UBT: | Yes |

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

Date Deposited: | 23 May 2023 06:30 |

Last Modified: | 23 May 2023 06:30 |

URI: | https://eref.uni-bayreuth.de/id/eprint/76511 |