## 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. |
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## 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 |
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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 (Computer Algebra) 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 |