A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
List decoding: algorithms and applications
ACM SIGACT News
Reconstructing curves in three (and higher) dimensional space from noisy data
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Better extractors for better codes?
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Robust locally testable codes and products of codes
Random Structures & Algorithms
Decoding interleaved Reed-Solomon codes over noisy channels
Theoretical Computer Science
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
Combinatorial construction of locally testable codes
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The tensor product of two codes is not necessarily robustly testable
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
Robust local testability of tensor products of LDPC codes
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
Geometric approach to higher weights
IEEE Transactions on Information Theory - Part 1
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
List decoding from erasures: bounds and code constructions
IEEE Transactions on Information Theory
List decoding of q-ary Reed-Muller codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
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We design the first efficient algorithms and prove new combinatorial bounds for list decoding tensor products of codes and interleaved codes. (1) We show that for every code, the ratio of its list decoding radius to its minimum distance stays unchanged under the tensor product operation (rather than squaring, as one might expect). This gives the first efficient list decoders and new combinatorial bounds for some natural codes including multivariate polynomials where the degree in each variable is bounded. (2) We show that for every code, its list decoding radius remains unchanged under m-wise interleaving for an integer m. This generalizes a recent result of Dinur.et.al, who proved such a result for interleaved Hadamard codes (equivalently, linear transformations). (3)Using the notion of generalized Hamming weights, we give better list size bounds for both tensoring and interleaving of binary linear codes. By analyzing the weight distribution of these codes, we reduce the task of bounding the list size to bounding the number of close-by low-rank codewords. For decoding linear transformations, using rank-reduction together with other ideas, we obtain tight list size bounds for small fields. Our results give better bounds on the list decoding radius than what is obtained from the Johnson bound, and yield rather general families of codes decodable beyond the Johnson bound.