Decoding of Lifted Affine-Invariant Codes
Information Theory
2021-04-22 v2 math.IT
Abstract
Lifted Reed-Solomon codes, a subclass of lifted affine-invariant codes, have been shown to be of high rate while preserving locality properties similar to generalized Reed-Muller codes, which they contain as subcodes. This work introduces a simple bounded distance decoder for (subcodes of) lifted affine-invariant codes that is guaranteed to decode up to almost half of their minimum distance. Further, long -ary lifted affine-invariant codes are shown to correct almost all error patterns of relative weight for .
Cite
@article{arxiv.2010.10433,
title = {Decoding of Lifted Affine-Invariant Codes},
author = {Lukas Holzbaur and Nikita Polyanskii},
journal= {arXiv preprint arXiv:2010.10433},
year = {2021}
}
Comments
This updated version fixes some minor typos and inaccuracies