Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules
Information Theory
2026-01-15 v2 math.IT
Number Theory
Abstract
We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progressions. Using our methods, we obtain a new infinite family of optimal rank-metric codes with rank-locality, i.e. every code in our family achieves the information theoretical bound for rank-metric codes with rank-locality.
Cite
@article{arxiv.2407.06081,
title = {Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules},
author = {Luca Bastioni and Mohamed O. Darwish and Giacomo Micheli},
journal= {arXiv preprint arXiv:2407.06081},
year = {2026}
}