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

Title data

Kohnert, Axel ; Zwanzger, Johannes:
New linear codes with prescribed group of automorphisms found by heuristic search.
In: Advances in Mathematics of Communications. Vol. 3 (2009) Issue 2 . - pp. 157-166.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2009.3.157

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Heuristic algorithm; Monte-Carlo; coding theory; linear codes; automorphism group; high minimum distance
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Jan 2015 08:11
Last Modified: 09 Feb 2015 12:26
URI: https://eref.uni-bayreuth.de/id/eprint/5791