<p style='text-indent:20px;'>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.</p>

中文翻译：

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从有理函数域的自同构构造最优秩度量码

<p style='text-indent:20px;'>我们定义了一类具有有限特征的有理函数域的自同构，并用它们来构造不同类型的最优线性秩度量码。第一个构造是在有理函数域上的广义 Gabidulin 代码。在有限域上减少这些代码，我们获得了不等同于广义扭曲 Gabidulin 代码的最大秩距离 (MRD) 代码。我们还构建了最优 Ferrers 图秩度量代码，进一步解决了 Etzion 和 Silberstein 的猜想。</p>