Locally recoverable codes on algebraic curves
Abstract
A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most ) other symbols of the codeword. In this paper we introduce a construction of LRC codes on algebraic curves, extending a recent construction of Reed-Solomon like codes with locality. We treat the following situations: local recovery of a single erasure, local recovery of multiple erasures, and codes with several disjoint recovery sets for every coordinate (the {\em availability problem}). For each of these three problems we describe a general construction of codes on curves and construct several families of LRC codes. We also describe a construction of codes with availability that relies on automorphism groups of curves.
Cite
@article{arxiv.1603.08876,
title = {Locally recoverable codes on algebraic curves},
author = {Alexander Barg and Itzhak Tamo and Serge Vladuts},
journal= {arXiv preprint arXiv:1603.08876},
year = {2016}
}
Comments
16pp. An extended abstract of this submission was posted earlier as arXiv:1501.04904 and was published in Proceedings of the 2015 IEEE International Symposium on Information Theory, Hong Kong, China, June 14-19, 2015, pp. 1252--1256