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arXiv · 1611.04447

Nuclei and automorphism groups of generalized twisted Gabidulin codes

Rocco Trombetti·Yue Zhou
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Abstract

Generalized twisted Gabidulin codes are one of the few known families of maximum rank matrix codes over finite fields. As a subset of m by n matrices, when m=n, the automorphism group of any generalized twisted Gabidulin code has been completely determined recently. In this paper, we consider the same problem for m<n. Under certain conditions on their parameters, we determine their middle nuclei and right nuclei, which are important invariants with respect to the equivalence for rank metric codes. Furthermore, we also use them to derive necessary conditions on the automorphisms of generalized twisted Gabidulin codes.

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BibTeXRIS

Rocco Trombetti, Yue Zhou. 2016-11-14. Nuclei and automorphism groups of generalized twisted Gabidulin codes. https://doi.org/10.1016/j.laa.2019.04.010

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