We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progressions. Using our methods, we obtain a new infinite family of optimal rank-metric codes with rank-locality, i.e. every code in our family achieves the information theoretical bound for rank-metric codes with rank-locality.

翻译：本文提出了一种利用全局域上Drinfeld模的算术理论以及多项式算术级数上的Dirichlet定理来构造秩度量码的新技术。通过我们的方法，我们获得了一个新的具有秩局部性的最优秩度量码无限族，即该族中的每个码都达到了具有秩局部性的秩度量码的信息理论界。