2020/10/20 by Holzbaur, Lukas, Polyanskii, Nikita
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2010.10433
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 q-ary lifted affine-invariant codes are shown to correct almost all error patterns of relative weight (q-1)/(q)-ε for ε>0.