Codes with hierarchical locality from covering maps of curves
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Locally recoverable (LRC) codes provide ways of recovering erased coordinates of the codeword without having to access each of the remaining coordinates. A subfamily of LRC codes with hierarchical locality (H-LRC codes) provides added flexibility to the construction by introducing several tiers of recoverability for correcting different numbers of erasures. We present a general construction of codes from maps between algebraic curves that have 2-level hierarchical locality and specialize it to several code families obtained from quotients of curves by a subgroup of the automorphism group, including rational, elliptic, Kummer, and Artin-Schreier curves. We also construct asymptotically good families of H-LRC codes from curves related to the Garcia-Stichtenoth tower.
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