Locally recoverable codes on surfaces
Abstract
A linear error correcting code is a subspace of a finite dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword can be deduced from the value of (certain) $r$ other coordinates of the codeword. These codes have found many recent applications, e.g., to distributed cloud storage. We will discuss the problem of constructing good locally recoverable codes and present some constructions using algebraic surfaces that improve previous constructions and sometimes provide codes that are optimal in a precise sense.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.13472
 Bibcode:
 2019arXiv191013472S
 Keywords:

 Computer Science  Information Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 Revised version