Alexander Barg, Kathryn Haymaker, Everett W. Howe, Gretchen L. Matthews, and Anthony Várilly-Alvarado: Locally recoverable codes from algebraic curves and surfaces, pp. 95–127 in: Algebraic Geometry for Coding Theory and Cryptography (E. W. Howe, K. E. Lauter, and J. L. Walker, eds.), Springer, Cham, 2017.

Official version here, preprint version here.

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.