A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Toward efficient agnostic learning
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Oblivious transfer and polynomial evaluation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
List decoding: algorithms and applications
ACM SIGACT News
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
A Quantum Goldreich-Levin Theorem with Cryptographic Applications
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Learning polynomials with queries: The highly noisy case
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Quantum hardcore functions by complexity-theoretical quantum list decoding
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
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Our task of quantum list decoding for a classical block code is to recover from a given quantumly corrupted codeword a short list containing all messages whose codewords have high "presence" in this quantumly corrupted codeword. All known families of efficiently quantum list decodable codes, nonetheless, have exponentially-small message rate. We show that certain generalized Reed-Solomon codes concatenated with Hadamard codes of polynomially-small rate and constant codeword alphabet size have efficient quantum list decoding algorithms, provided that target codewords should have relatively high presence in a given quantumly corrupted codeword.