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

翻译：我们定义了一组有限特性的合理功能领域的自定性,并使用它们来构建不同类型的最佳线性分级代码。第一种构造是通用的加比杜林代码对合理功能领域。将这些代码缩小到有限功能领域,我们获得最高级距离代码,这些代码不等同于普遍扭曲的加比杜林代码。我们还构建了最佳的Ferres图表级分级代码,这些代码进一步解决了Etzion和Silberstein的推测。