The paper proves that the Gibbs decoder for Reed-Muller codes can have super-polynomial mixing time on certain typical received sequences, so it is not a worst-case polynomial-time decoder.
Reed–muller codes achieve capacity on erasure ch annels,
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On the Worst-Case Complexity of Gibbs Decoding for Reed--Muller Codes
The paper proves that the Gibbs decoder for Reed-Muller codes can have super-polynomial mixing time on certain typical received sequences, so it is not a worst-case polynomial-time decoder.