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

Title data

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

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Automorphism group; canonization; coding theory; error-correcting code; group action; representative; semilinear isometry
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
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 09:55
Last Modified: 22 Jan 2015 09:55
URI: https://eref.uni-bayreuth.de/id/eprint/5832