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Canonization of linear codes over ℤ₄

Title data

Feulner, Thomas:
Canonization of linear codes over ℤ₄.
In: Advances in Mathematics of Communications. Vol. 5 (2011) Issue 2 . - pp. 245-266.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2011.5.245

Project information

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

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Automorphism group, canonization, coding theory, group action, representative, isometry, Z4-linear code.
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 09:52
Last Modified: 22 Jan 2015 09:52
URI: https://eref.uni-bayreuth.de/id/eprint/5833