We establish a connection between Drinfeld modules and rank-metric codes, focusing on the case of semifield codes. Our method constructs rank-metric codes from linear subspaces of endomorphisms of a Drinfeld module acting on torsion submodules. We show that Sheekey's construction [She20] fits naturally into this framework, yielding a short conceptual proof of one of his main results. We then give a new construction of infinite families of semifield codes arising from Drinfeld modules defined over finite fields.

翻译：我们建立了Drinfeld模与秩度量码之间的联系，重点关注半域码的情形。我们的方法从Drinfeld模作用于挠子模的自同态线性子空间构造秩度量码。我们证明Sheekey的构造[She20]自然地适用于这一框架，从而为其主要结论之一提供了简短的概念性证明。随后，我们给出一种基于有限域上定义的Drinfeld模构造半域码无穷族的新方法。