Rank metric codes from Drinfeld modules
Giacomo Micheli, Mihran Papikian

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
