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The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes

Titelangaben

Feulner, Thomas:
The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes.
In: Advances in Mathematics of Communications. Bd. 3 (2009) Heft 4 . - S. 363-383.
ISSN 1930-5346
DOI: 10.3934/amc.2009.3.363

Abstract

The main aim of the classification of linear codes is the evaluation of complete lists of representatives of the isometry classes. These classes are mostly defined with respect to linear isometry, but it is well known that
there is also the more general definition of semilinear isometry taking the field automorphisms into account. This notion leads to bigger classes so the data becomes smaller. Hence we describe an algorithm that gives canonical repre-
sentatives of these bigger classes by calculating a unique generator matrix to a given linear code, in a well defined manner.

The algorithm is based on the partitioning and refinement idea which is also used to calculate the canonical labeling of a graph [12] and it similarly returns the automorphism group of the given linear code. The time needed by the implementation of the algorithm is comparable to Leon’s program [10] for the calculation of the linear automorphism group of a linear code, but it additionally provides a unique representative and the automorphism group with
respect to the more general notion of semilinear equivalence. The program can be used online under http://www.algorithm.uni-bayreuth.de/en/research/
Coding_Theory/CanonicalForm/index.html.

Weitere Angaben

Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Keywords: Automorphism group; canonization; coding theory; error-correcting code; group action; representative; semilinear isometry
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 09:55
Letzte Änderung: 22 Jan 2015 09:55
URI: https://eref.uni-bayreuth.de/id/eprint/5832