Rank metric codes from Drinfeld modules

TL;DR

This paper links Drinfeld modules to rank-metric codes, providing new constructions of semifield codes and a conceptual proof of Sheekey's results, advancing algebraic coding theory.

Contribution

It introduces a novel connection between Drinfeld modules and rank-metric codes, including new infinite semifield code constructions and a conceptual proof of existing results.

Findings

Sheekey's construction fits into the Drinfeld module framework

New infinite families of semifield codes are constructed from Drinfeld modules

A short, conceptual proof of Sheekey's main result is provided

Abstract

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.