|Locally recoverable codes on algebraic curves |
Auteur(s): Alexander Barg, Itzhak Tamo, Serge Vladut, Vladuts S.
Conference: . IEEE Int. Sympos. Inform. Theory. 2015 (Hong Kong, HK, 2015-06)
Ref HAL: hal-01220138_v1
Exporter : BibTex | endNote
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.