Rank metric codes from Drinfeld modules
For coding theory researchers, this work offers a new algebraic framework for constructing rank-metric codes, though the results are incremental.
The paper connects Drinfeld modules to rank-metric codes, constructing semifield codes from endomorphisms of Drinfeld modules. It provides a conceptual proof of a known result and produces new infinite families of semifield codes.
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.