List-decoding algorithms for lifted codes
Abstract
Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable to the known algorithms for Reed-Muller codes), but with significantly better rate. We give efficient algorithms for list-decoding and local list-decoding of lifted codes. Our algorithms are based on a new technical lemma, which says that codewords of lifted codes are low degree polynomials when viewed as univariate polynomials over a big field (even though they may be very high degree when viewed as multivariate polynomials over a small field).
Cite
@article{arxiv.1412.0305,
title = {List-decoding algorithms for lifted codes},
author = {Alan Guo and Swastik Kopparty},
journal= {arXiv preprint arXiv:1412.0305},
year = {2017}
}
Comments
15 pages, no figures. Revision expands the proof of the main technical theorem, Theorem 3.2