%0 Conference Proceedings
%T Locally recoverable codes on algebraic curves
%+ Dobrushin laboratory of Mathematics (IITP)
%+ Institut de MathÃ©matiques de Marseille (I2M)
%A Alexander, Barg
%A Itzhak, Tamo
%A Serge, Vladut
%A Vladuts, Serge
%< avec comitÃ© de lecture
%( Proc. IEEE Int. Sympos. Inform. Theory.
%B . IEEE Int. Sympos. Inform. Theory. 2015
%C Hong Kong, Hong Kong SAR China
%P 1252-1256
%8 2015-06
%D 2015
%Z Mathematics [math]/Information Theory [math.IT]Conference papers
%X 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.
%G English
%L hal-01220138
%U https://hal.archives-ouvertes.fr/hal-01220138
%~ CNRS
%~ EC-MARSEILLE
%~ INSMI
%~ I2M-2014-
%~ I2M
%~ UNIV-AMU
%~ TEST-AMU