Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Decoding of Reed-Muller codes with polylogarithmic complexity
WISICT '04 Proceedings of the winter international synposium on Information and communication technologies
Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Maximum-likelihood decoding of Reed-Solomon codes is NP-hard
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Query-efficient algorithms for polynomial interpolation over composites
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
List-decoding reed-muller codes over small fields
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Decodability of group homomorphisms beyond the johnson bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On agnostic boosting and parity learning
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Exposure-Resilient Extractors and the Derandomization of Probabilistic Sublinear Time
Computational Complexity
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Improvements on the Johnson bound for Reed-Solomon codes
Discrete Applied Mathematics
The Security of All Bits Using List Decoding
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Extracting Computational Entropy and Learning Noisy Linear Functions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Authenticated error-correcting codes with applications to multicast authentication
ACM Transactions on Information and System Security (TISSEC)
Nearly one-sided tests and the Goldreich-Levin predicate
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
A public key encryption scheme based on the polynomial reconstruction problem
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Local list-decoding and testing of random linear codes from high error
Proceedings of the forty-second ACM symposium on Theory of computing
Hardness of Reconstructing Multivariate Polynomials over Finite Fields
SIAM Journal on Computing
Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding
SIAM Journal on Computing
Some recent results on local testing of sparse linear codes
Property testing
Some recent results on local testing of sparse linear codes
Property testing
Three XOR-lemmas - an exposition
Studies in complexity and cryptography
Computational randomness from generalized hardcore sets
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Public-key encryption schemes with auxiliary inputs
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Local decoding and testing for homomorphisms
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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Given a function f mapping n-variate inputs from a finite field F into F, we consider the task of reconstructing a list of all n-variate degree d polynomials that agree with f on a tiny but nonnegligible fraction, $\delta$, of the input space. We give a randomized algorithm for solving this task. The algorithm accesses f as a black box and runs in time polynomial in ${\frac{n}\d}$ and exponential in d, provided $\delta$ is $\Omega(\sqrt{d/|F|})$. For the special case when d = 1, we solve this problem for all $\epsilon\eqdef\delta - \frac1{|F|} 0$. In this case the running time of our algorithm is bounded by a polynomial in $\frac1\e$ and $n$. Our algorithm generalizes a previously known algorithm, due to Goldreich and Levin [in Proceedings of the 21st Annual ACM Symposium on Theory of Computing, Seattle, WA, ACM Press, New York, 1989, pp. 25--32.], that solves this task for the case when F = GF(2) (and d = 1).In the process we provide new bounds on the number of degree $d$ polynomials that may agree with any given function on $\d \geq \sqrt{d/|F|}$ fraction of the inputs. This result is derived by generalizing a well-known bound from coding theory on the number of codewords from an error-correcting code that can be "close" to an arbitrary word; our generalization works for codes over arbitrary alphabets, while the previous result held only for binary alphabets.