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Codes With Hierarchical Locality From Covering Maps of Curves.
- Source :
- IEEE Transactions on Information Theory; Oct2019, Vol. 65 Issue 10, p6056-6071, 16p
- Publication Year :
- 2019
-
Abstract
- 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 with 2-level hierarchical locality from maps between algebraic curves 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 further address the question of H-LRC codes with availability, and suggest a general construction of such codes from fiber products of curves. Detailed calculations of parameters for H-LRC codes with availability are performed for Reed–Solomon- and Hermitian-like code families. Finally, we construct asymptotically good families of H-LRC codes from curves related to the Garcia–Stichtenoth tower. [ABSTRACT FROM AUTHOR]
- Subjects :
- AUTOMORPHISMS
AUTOMORPHISM groups
ALGEBRAIC curves
CIPHERS
REED-Solomon codes
CURVES
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 138733205
- Full Text :
- https://doi.org/10.1109/TIT.2019.2919830