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New linear codes with prescribed group of automorphisms found by heuristic search

Titelangaben

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: 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