Codes with hierarchical locality from covering maps of curves
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.
READ FULL TEXT