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Canonization of linear codes over ℤ₄

Titelangaben

Feulner, Thomas:
Canonization of linear codes over ℤ₄.
In: Advances in Mathematics of Communications. Bd. 5 (2011) Heft 2 . - S. 245-266.
ISSN 1930-5346
DOI: 10.3934/amc.2011.5.245

Angaben zu Projekten

Projektfinanzierung: The research of the author was supported by a scholarship awarded by the Bayerische Eliteförderung.

Abstract

Two linear codes C, C' ≤ ℤ₄^n 4 are equivalent if there is a permutation π ∈ S_n of the coordinates and a vector φ ∈ {1, 3}^n of column multiplications such that (φ;π)C = C'. This generalizes the notion of code equivalence of linear codes over finite fields.

In a previous paper, the author has described an algorithm to compute the canonical form of a linear code over a finite field. In the present paper, analgorithm is presented to compute the canonical form as well as the automorphism group of a linear code over ℤ₄. This solves the isomorphism problem for ℤ₄-linear codes. An efficient implementation of this algorithm is described and some results on the classification of linear codes over ℤ₄ for small parameters are discussed.

Weitere Angaben

Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Keywords: Automorphism group, canonization, coding theory, group action, representative, isometry, Z4-linear code.
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 09:52
Letzte Änderung: 22 Jan 2015 09:52
URI: https://eref.uni-bayreuth.de/id/eprint/5833