Recursive decoding of projective Reed-Muller codes
Rodrigo San-Jos\'e
TL;DR
This paper introduces a recursive decoding algorithm for projective Reed-Muller codes that leverages affine Reed-Muller decoders, achieving the highest known error correction capability and analyzing its complexity.
Contribution
It presents the first recursive decoding method for projective Reed-Muller codes that matches their maximum error correction potential.
Findings
Maximum error correction capability achieved
Decoding complexity matches that of affine Reed-Muller decoders
Algorithm extends the decoding performance of projective Reed-Muller codes
Abstract
We give a recursive decoding algorithm for projective Reed-Muller codes making use of a decoder for affine Reed-Muller codes. We determine the number of errors that can be corrected in this way, which is the current highest for decoders of projective Reed-Muller codes. We show when we can decode up to the error correction capability of these codes, and we compute the order of complexity of the algorithm, which is given by that of the chosen decoder for affine Reed-Muller codes.
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