How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Journal of the ACM (JACM)
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
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Optimal Lower Bounds for 2-Query Locally Decodable Linear Codes
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Better Lower Bounds for Locally Decodable Codes
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
List-Decoding Using The XOR Lemma
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
Lower bounds for linear locally decodable codes and private information retrieval
Computational Complexity
The complexity of hardness amplification and derandomization
The complexity of hardness amplification and derandomization
Towards 3-query locally decodable codes of subexponential length
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Verifying and decoding in constant depth
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
Uniform direct product theorems: simplified, optimized, and derandomized
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A lower bound on list size for list decoding
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
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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We study the complexity of locally list-decoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over 茂戮驴(1/茂戮驴) bits is essentially equivalent to locally list-decoding binary codes from relative distance 1/2 茂戮驴 茂戮驴with list size at most poly (1/茂戮驴). That is, a local-decoder for such a code can be used to construct a circuit of roughly the same size and depth that computes majority on 茂戮驴(1/茂戮驴) bits. On the other hand, there is an explicit locally list-decodable code with these parameters that has a very efficient (in terms of circuit size and depth) local-decoder that uses majority gates of fan-in 茂戮驴(1/茂戮驴).Using known lower bounds for computing majority by constant depth circuits, our results imply that every constant-depth decoder for such a code must have size almost exponential in 1/茂戮驴(this extends even to sub-exponential list sizes). This shows that the list-decoding radius of the constant-depth local-list-decoders of Goldwasser et al.[STOC07] is essentially optimal.