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

TL;DR

This paper presents a novel construction of optimal rank-metric codes with rank-locality using Drinfeld modules and number theory, achieving the theoretical bounds for this class of codes.

Contribution

It introduces a new technique based on Drinfeld modules and polynomial arithmetic progressions to construct infinite families of optimal rank-metric codes with rank-locality.

Findings

Constructed an infinite family of optimal rank-metric codes with rank-locality.

Codes achieve the information-theoretic bounds for rank-metric codes with rank-locality.

Utilized arithmetic theory of Drinfeld modules and Dirichlet Theorem in code construction.

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.