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Kohnert, Axel:
(l, s)-extension of linear codes.
In: Discrete Mathematics.
Bd. 309
(2009)
Heft 2
.
- S. 412-417.
ISSN 0012-365X
DOI: https://doi.org/10.1016/j.disc.2007.12.028
Abstract
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n, k. Among these new codes there is an optimal ternary [88, 8, 54]_3 code.
We develop an algorithm, which starts with already good codes C, i.e. codes with high minimum distance d for given length n and dimension k over the field G F(q). The algorithm is based on the newly defined (l, s)-extension. This is a generalization of the well-known method of adding a parity bit in the case of a binary linear code of odd minimum weight. (l, s)-extension tries to extend the generator matrix of C by adding l columns with the property that at least s of the l letters added to each of the codewords of minimum weight in C are different from 0. If one finds such columns the minimum distance of the extended code is d + s provided that the second smallest weight in C was at least d + s. The question whether such columns exist can be settled using a Diophantine system of equations.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik II (Computeralgebra) Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 22 Jan 2015 08:20 |
| Letzte Änderung: | 05 Dec 2023 13:21 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/5792 |