Mathematical LoRE: Local Recovery of Erasures using Polynomials, Curves, Surfaces, and Liftings

Abstract

Employing underlying geometric and algebraic structures allows for constructing bespoke codes for local recovery of erasures. We survey techniques for enriching classical codes with additional machinery, such as using lines or curves in projective space for local recovery sets or products of curves to enhance the availability of data.

IEEE BITS the Information Theory Magazine, to appear