On the list recoverability of randomly punctured codes
Combinatorics
2020-07-07 v3 Computational Complexity
Discrete Mathematics
Information Theory
math.IT
Abstract
We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.
Keywords
Cite
@article{arxiv.2005.02478,
title = {On the list recoverability of randomly punctured codes},
author = {Ben Lund and Aditya Potukuchi},
journal= {arXiv preprint arXiv:2005.02478},
year = {2020}
}
Comments
13 pages, several changes in introductory sections