## Title data

Körner, Theresa ; Kurz, Sascha:

**Partial results on the possible effective lengths of divisible codes.**

2023

*Event:* Workshop Combinatorics in Digital Communication
, 19.-21.04.2023
, Eindhoven, Netherlands.

(Conference item: Workshop
,
Speech
)

## Related URLs

## Abstract in another language

A linear code C over GF(q) is called ∆-divisible if the Hamming weights wt(c) of all codewords care divisible by ∆. Divisible codes were first studied by Harold Ward.

When we associate each subspace U in PG(n−1,q) with its characteristic function that maps each point

to an non-negative integer multiplicity

we get a connection between divisible codes and Galois geometries. A mapping from the pointset of

PG(n − 1, q) to the integers is called ∆-divisible if the corresponding linear code associated with the multiset of

points is ∆-divisible.

There exist some upper bounds for partial spreadsusing that the corresponding divisible codes must be projective. For the characterization result for the possible (effective) lengths of q^r-divisible codes quite large point multiplicities are needed on the constructive side, so there is a requirement for more refined results on different parameters e.g. the maximum possible point multiplicities

or the dimension. In this talk I present some partial results on the possible effective lengths of divisible

codes with extra constraints.

## Further data

Item Type: | Conference item (Speech) |
---|---|

Refereed: | No |

Additional notes: | Speaker: Theresa Körner |

Keywords: | divisible codes; linear codes; partial spreads; Galois Geometry; Subspace Codes |

Subject classification: | Mathematics Subject Classification Code: 94B05 (51E23) |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science 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: | 26 Apr 2023 08:16 |

Last Modified: | 26 Apr 2023 08:16 |

URI: | https://eref.uni-bayreuth.de/id/eprint/76103 |