Alexander Barg, Kathryn Haymaker, Everett W. Howe, Gretchen L. Matthews, and Anthony Várilly-Alvarado: Locally recoverable codes from algebraic curves and surfaces, Algebraic Geometry for Coding Theory and Cryptography (E.W. Howe, K.E. Lauter, and J.L. Walker, eds.), Springer, Cham, 2017, to appear.

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.