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Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules (2407.06081v1)
Published 8 Jul 2024 in cs.IT, math.IT, and math.NT
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.