Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules
<|reference_start|>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.<|reference_end|>
@article{bastioni2024optimal,
    title={Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules},
    author={Luca Bastioni and Mohamed O. Darwish and Giacomo Micheli},
    journal={arXiv preprint arXiv:2407.06081},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.06081},
    primaryClass={cs.IT math.IT math.NT}
}