## Title data

Kurz, Sascha ; Mattheus, Sam:

**A Generalization of the Cylinder Conjecture for Divisible Codes.**

*In:* IEEE Transactions on Information Theory.
Vol. 68
(2022)
Issue 4
.
- pp. 2281-2289.

ISSN 0018-9448

DOI: https://doi.org/10.1109/TIT.2021.3134201

## Abstract in another language

We extend the original cylinder conjecture on point sets in affine three-dimensional space to the more general framework of divisible linear codes over GF(q) and their classification. Through a mix of linear programming, combinatorial techniques and computer enumeration, we investigate the structural properties of these codes. In this way, we can prove a reduction theorem for a generalization of the cylinder conjecture, show some instances where it does not hold and prove its validity for small values of q. In particular, we correct a flawed proof for the original cylinder conjecture for q=5 and present the first proof for q=7.

## Further data

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

Refereed: | Yes |

Keywords: | cylinder conjecture; linear codes; divisible codes |

Subject classification: | Mathematics Subject Classification Code: 05B25 (51D20 51E22) |

Institutions of the University: | 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: | 22 Mar 2022 10:15 |

Last Modified: | 22 Mar 2022 10:15 |

URI: | https://eref.uni-bayreuth.de/id/eprint/68965 |