Maximum-likelihood decoding of Reed-Solomon codes is NP-hard

@article{Guruswami2004MaximumlikelihoodDO,
  title={Maximum-likelihood decoding of Reed-Solomon codes is NP-hard},
  author={Venkatesan Guruswami and Alexander Vardy},
  journal={Electron. Colloquium Comput. Complex.},
  year={2004}
}
  • V. Guruswami, A. Vardy
  • Published 3 May 2004
  • Computer Science, Mathematics
  • Electron. Colloquium Comput. Complex.
Maximum-likelihood decoding is one of the central problems in coding theory. It has been known for over 25 years that maximum-likelihood decoding of general linear codes is NP-hard. Nevertheless, it was so far unknown whether maximum-likelihood decoding remains hard for any specific family of codes with nontrivial algebraic structure. In this paper, we prove that maximum-likelihood decoding is NP-hard for the family of Reed-Solomon codes. We moreover show that maximum-likelihood decoding of… 
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