## Title data

Kurz, Sascha:

**Divisible minimal codes.**

Bayreuth
,
2023
. - 14 p.

DOI: https://doi.org/10.15495/EPub_UBT_00007346

## Abstract in another language

Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a k-dimensional linear code over GF(q) is denoted by m(k,q). Here we determine m(7,2), m(8,2), and m(9,2), as well as full classifications of all codes attaining m(k,2) for k<=7 and those attaining m(9,2). For m(11,2) and m(12,2) we give improved upper bounds. It turns out that in many cases attaining extremal codes have the property that the weights of all codewords are divisible by some constant &\Delta;>1. So, here we study the minimum lengths of minimal codes where we additionally assume that the weights of the codewords are divisible by &\Delta;.

## Further data

Item Type: | Preprint, postprint |
---|---|

Keywords: | minimal codes; divisible 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 Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties |

Result of work at the UBT: | Yes |

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

Date Deposited: | 09 Dec 2023 22:00 |

Last Modified: | 11 Dec 2023 10:17 |

URI: | https://eref.uni-bayreuth.de/id/eprint/88011 |