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- Locally recoverable codes on algebraic curves hal link

Auteur(s): Alexander Barg, Itzhak Tamo, Serge Vladut, Vladuts S.

Conference: . IEEE Int. Sympos. Inform. Theory. 2015 (Hong Kong, HK, 2015-06)
Actes de conférence: Proc. IEEE Int. Sympos. Inform. Theory., vol. p.1252-1256 (2015)


Ref HAL: hal-01220138_v1
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Résumé:

A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. A family of linear LRC codes that generalize the classic construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A. Barg. In this paper we extend this construction to codes on algebraic curves. We give a general construction of LRC codes on curves and compute some examples, including asymptotically good families of codes derived from the Garcia- Stichtenoth towers. The local recovery procedure is performed by polynomial interpolation over r coordinates of the codevector. We also obtain a family of Hermitian codes with two disjoint recovering sets for every symbol of the codeword.