Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules

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.

💡 Research Summary

The paper presents a novel construction of rank‑metric codes that simultaneously achieve optimal distance and rank‑locality, by exploiting the arithmetic of Drinfeld modules together with Dirichlet’s theorem on polynomial arithmetic progressions.

Motivation and Background
Rank‑metric codes are essential for correcting errors modeled as low‑rank matrices, with applications ranging from network coding to cryptography. In distributed storage, locality enables the recovery of a lost node by accessing only a small subset of other nodes. Extending locality to the rank‑metric setting (rank‑locality) is crucial for handling criss‑cross failures in data centers. Prior work (e.g.,