  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.
