Highly resilient correctors for polynomials
Information Processing Letters
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Algorithmic complexity in coding theory and the minimum distance problem
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
The Parametrized Complexity of Some Fundamental Problems in Coding Theory
SIAM Journal on Computing
Learning Polynomials with Queries: The Highly Noisy Case
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
The inapproximability of lattice and coding problems with preprocessing
Journal of Computer and System Sciences - Special issue on computational complexity 2002
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Hardness of approximating the minimum distance of a linear code
IEEE Transactions on Information Theory
Improved inapproximability of lattice and coding problems with preprocessing
IEEE Transactions on Information Theory
On deciding deep holes of Reed-Solomon codes
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A low complexity iterative technique for soft decision decoding of reed-solomon codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
On error correction in the exponent
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Algorithms for modular counting of roots of multivariate polynomials
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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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 Reed-Solomon codes remains hard even with unlimited preprocessing, thereby strengthening a result of Bruck and Naor.