An error correcting code is a subspace of knkn, where kk is a finite field. Such a code is said to be locally recoverable with locality rr if, for every coordinate of a codeword, its value can be deduced from the value of (certain) rr other coordinates. These codes have found many recent applications, e.g., to cloud storage. We will discuss the problem of constructing good locally recoverable codes and present some constructions using algebraic surfaces that sometimes provide codes that are optimal in some precise sense.
Joint work with C. Salgado and A. Varilly Alvarado.