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Locally recoverable codes from algebraic curves and surfaces
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.