Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Self-testing/correcting for polynomials and for approximate functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Highly resilient correctors for polynomials
Information Processing Letters
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
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
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
Breaking the O(n1/(2k-1)) Barrier for Information-Theoretic Private Information Retrieval
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Upper Bound on Communication Complexity of Private Information Retrieval
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Optimal Lower Bounds for 2-Query Locally Decodable Linear Codes
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Better Lower Bounds for Locally Decodable Codes
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
An optimal lower bound for 2-query locally decodable linear codes
Information Processing Letters
IEEE Transactions on Information Theory - Part 1
Low rate is insufficient for local testability
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
| Hi-index | 0.00 |
An error-correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan [On the efficiency of local decoding procedures for error correcting codes, STOC, 2000, pp. 80-86] showed that any such code C : {0, 1}n → Σm with a decoding algorithm that makes at most q probes must satisfy m = Ω((n/log |Σ|)q/(q-1)). They assumed that the decoding algorithm is non-adaptive, and left open the question of proving similar bounds for adaptive decoders. We show m = Ω((n/log |Σ|)q/(q-1)) without assuming that the decoder is nonadaptive.