Constructions of optimal rank-metric codes from automorphisms of rational function fields

We define a class of automorphisms rational function fields finite characteristic and employ these to construct different types optimal linear rank-metric codes. The first construction is generalized Gabidulin codes over fields. Reducing fields, we obtain maximum rank distance (MRD) which are not equivalent twisted also Ferrers diagram settles further conjecture by Etzion Silberstein.