2021/05/07 by D. Shivakrishna, Shivakrishna, D., Aaditya M. Nair +3
Computer Science · #Advanced Data Storage Technologies #Cellular Automata and Applications #Cryptography and Data Security #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2105.03328
openalex publication_date 2021/05/07 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with locality. The notion of locality has been extended to hierarchical locality, which allows for locality to gradually increase in levels with the increase in the number of erasures. We consider the locality constraints imposed by codes with two-level hierarchical locality and define maximally recoverable codes with data-local and local hierarchical locality. We derive certain properties related to their punctured codes and minimum distance. We give a procedure to construct hierarchical data-local MRCs from hierarchical local MRCs. We provide a construction of hierarchical local MRCs for all parameters. We also give constructions of MRC with hierarchical locality for some parameters, whose field size is smaller than that of known constructions for general parameters. We also derive a field size lower bound on MRC with hierarchical locality.