## Title data

Kiermaier, Michael ; Kurz, Sascha:

**On the lengths of divisible codes.**

*In:* IEEE Transactions on Information Theory.
Vol. 66
(2020)
Issue 7
.
- pp. 4051-4060.

ISSN 0018-9448

DOI: https://doi.org/10.1109/TIT.2020.2968832

## Project information

Project title: |
Project's official title Project's id Integer Linear Programming Models for Subspace Codes and Finite Geometry No information |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

In this article, the effective lengths of all q^r-divisible linear codes over GF(q) with a non-negative integer r are determined. For that purpose, the S_q(r)-adic expansion of an integer n is introduced. It is shown that there exists a q^r-divisible GF(q)-linear code of effective length n if and only if the leading coefficient of the S_q(r)-adic expansion of n is non-negative. Furthermore, the maximum weight of a q^r-divisible code of effective length n is at most the cross-sum of the S_q(r)-adic expansion of n.

This result has applications in Galois geometries.

A recent theorem of Nastase and Sissokho on the maximum size of a partial spread follows as a corollary. Furthermore, we get an improvement of the Johnson bound for constant dimension subspace codes.

## Further data

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

Refereed: | Yes |

Keywords: | divisible codes; constant dimension codes; partial spreads |

Subject classification: | Mathematics Subject Classification Code: 51E23 (05B40) |

Institutions of the University: | 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 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: | 23 Jun 2020 06:52 |

Last Modified: | 02 Feb 2022 13:49 |

URI: | https://eref.uni-bayreuth.de/id/eprint/55583 |