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Kohnert, Axel ; Zwanzger, Johannes:
New linear codes with prescribed group of automorphisms found by heuristic search.
In: Advances in Mathematics of Communications.
Bd. 3
(2009)
Heft 2
.
- S. 157-166.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2009.3.157
Abstract
In this paper, we present a new heuristic algorithm for solving certain systems of Diophantine inequalities. A variant which involves Monte-Carlo search is also applyable to more general problems. Our goal was the construction of point sets in PG(k-1, q) with fixed cardinality and small
maximal intersection number with the lines. These points sets correspond to k-dimensional linear codes over F_q with high minimum distance. We obtained them by prescribing a certain nontrivial subgroup of GL(k, q) to be contained
in their automorphism group. Following a method which was first introduced by Kramer and Mesner in the 1970s, this allows a strong reduction in the size of the corresponding Diophantine systems. Doing so we found a lot of new
record breaking linear codes for the cases q = 2, 3, 4, 5, 7, 8, 9 from which at least 6 are optimal.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | Heuristic algorithm; Monte-Carlo; coding theory; linear codes; automorphism group; high minimum distance |
| 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 08:11 |
| Letzte Änderung: | 09 Feb 2015 12:26 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/5791 |