A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Pseudorandom generators without the XOR Lemma (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Learning Polynomials with Queries: The Highly Noisy Case
SIAM Journal on Discrete Mathematics
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Theoretical Computer Science
Noise-tolerant learning, the parity problem, and the statistical query model
Journal of the ACM (JACM)
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Sub-constant error low degree test of almost-linear size
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New Results for Learning Noisy Parities and Halfspaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
Low-degree tests at large distances
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Sparse Random Linear Codes are Locally Decodable and Testable
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the fortieth annual ACM symposium on Theory of computing
Symposium on Theory of Computing Conference 2008
List-decoding reed-muller codes over small fields
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Uniform direct product theorems: simplified, optimized, and derandomized
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Locally Testing Direct Product in the Low Error Range
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Tolerant Linearity Testing and Locally Testable Codes
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory
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We study the local testability of linear codes. Our approach is based on a reformulation of this question in the language of tolerant linearity testing under a non-uniform distribution. We then study the question of linearity testing under non-uniform distributions directly, and give a sufficient criterion for linearity to be tolerantly testable under a given distribution.We show that several natural classes of distributions satisfy this criterion (such as product distributions and low Fourier-bias distributions), thus showing that linearity is tolerantly testable under these distributions. This in turn implies that the corresponding codes are locally testable. For the case of random sparse linear codes, we show the testability and decodability of such codes in the presence of very high noise rates. More precisely, we show that any linear code in F2n which is: - sparse (i.e., has only poly(n) codewords) - unbiased (i.e., each nonzero codeword has Hamming weight in (1/2- n-γ, 1/2 + n-γ for some constant γ ≥ 0) can be locally tested and locally list decoded from (1/2-ε)-fraction errors using only poly(1/ε) queries to the received word. This simultaneously simplifies and strengthens a result of Kaufman and Sudan, who gave a local tester and local (unique) decoder for such codes from some constant fraction of errors. For the case of Dual BCH codes, our algorithms can also be made to run in sublinear time. Building on the methods used for the local algorithms, we also give sub-exponential time algorithms for list-decoding arbitrary unbiased (but not necessarily sparse) linear codes in the high-error regime.