Abstract
Generalized twisted Gabidulin codes are one of the few known families of maximum rank metric codes over finite fields. As a subset of m×n matrices, when m=n, the automorphism group of any generalized twisted Gabidulin code has been completely determined by the authors in [20]. 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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