Rank metric codes from Drinfeld modules
Number Theory
2026-04-14 v2 Information Theory
Combinatorics
math.IT
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.
Keywords
Cite
@article{arxiv.2601.03653,
title = {Rank metric codes from Drinfeld modules},
author = {Giacomo Micheli and Mihran Papikian},
journal= {arXiv preprint arXiv:2601.03653},
year = {2026}
}
Comments
20 pages