2024/07/08 by Bastioni, Luca, Darwish, Mohamed O., Micheli, Giacomo · 1 citation
#11T06 #14G50 #68P30 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2407.06081
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.