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: https://doi.org/10.3934/amc.2011.5.245

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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.