The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes
Thomas Feulner - Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany (email)
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 representatives of these bigger classes by calculating a unique generator matrix to a given linear code, in a well defined manner.
Keywords: Automorphism group, canonization, coding theory, error-correcting
code, group action, representative, semilinear isometry.
Received: May 2009; Revised: September 2009; Published: November 2009.
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