Preprint version: arXiv:1701.05212 [cs.IT].

A *locally recoverable code* is a code over a finite alphabet such that the value of any
single coordinate of a codeword can be recovered from the values of a small subset of other
coordinates. Building on work of Barg, Tamo, and Vlăduţ, we present several constructions
of locally recoverable codes from algebraic curves and surfaces.