English

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

R2 v1 2026-07-01T08:53:50.956Z