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Chubenko, Vladimir ; Kurz, Sascha:
Divisible minimal codes.
In: Serdica Journal of Computing.
Bd. 18
(2024)
Heft 2
.
- S. 97-124.
ISSN 1312-6555
Abstract
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 at most 7 and those attaining m(9, 2). We give improved upper bounds for m(k, 2) for
all dimensions k between 10 and 17. It turns out that in many cases the attaining extremal codes have the property that the weights of all codewords are divisible by some
constant ∆ > 1. So, here we study the minimum lengths of minimal codes where we additionally assume that the weights of the codewords are divisible by ∆. As a byproduct we also give a few binary linear codes improving the best known lower bound for the minimum distance.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | minimal codes; divisible codes; optimal codes; quasi-cyclic codes;
acute sets |
| Fachklassifikationen: | Mathematics Subject Classification 2020: 94B05 (51E23) |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Wirtschaftsmathematik |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 000 Informatik,Informationswissenschaft, allgemeine Werke > 004 Informatik 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 24 Jun 2025 11:34 |
| Letzte Änderung: | 24 Jun 2025 11:34 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/93969 |