Locally recoverable codes and algebraic surfaces

Felipe Voloch

Affiliation:

University of Canterbury

Date:

Wed, 24/10/2018 - 1:00pm

Venue:

RC-4082, The Red Centre, UNSW

Abstract:

An error correcting code is a subspace of $k^n$, where $k$ is a finite field. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate of a codeword, its value can be deduced from the value of (certain) $r$ 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.