We establish a connection between Drinfeld modules and rank metric codes, focusing on the case of semifield codes. Our framework constructs rank metric codes from linear subspaces of endomorphisms of a Drinfeld module, using tools such as characteristic polynomials on Tate modules and the Chebotarev density theorem. We show that Sheekey's construction [She20] fits naturally into this setting, 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：本文建立了Drinfeld模与秩度量码之间的联系，重点研究半域码的情形。我们的框架利用Drinfeld模自同态线性子空间构造秩度量码，其中运用了Tate模上的特征多项式与Chebotarev密度定理等工具。我们证明Sheekey的构造[She20]可自然地嵌入该框架，从而为其主要结果之一提供了简洁的概念性证明。进一步地，我们给出了一类新的无限族半域码构造，这些码源于有限域上定义的Drinfeld模。