English

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 qq-ary lifted affine-invariant codes are shown to correct almost all error patterns of relative weight q1qϵ\frac{q-1}{q}-\epsilon for ϵ>0\epsilon>0.

Keywords

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

R2 v1 2026-06-23T19:29:44.454Z