Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules
Luca Bastioni, Mohamed O. Darwish, Giacomo Micheli · SIAM Journal on Applied Algebra and Geometry · 2026
Abstract. We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules and the 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.