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
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
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
General constructions for information-theoretic private information retrieval
Journal of Computer and System Sciences
An optimal lower bound for 2-query locally decodable linear codes
Information Processing Letters
Lower bounds for adaptive locally decodable codes
Random Structures & Algorithms
A tight lower bound for restricted PIR protocols
Computational Complexity
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Towards 3-query locally decodable codes of subexponential length
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Interpolation of depth-3 arithmetic circuits with two multiplication gates
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
A quadratic lower bound for three-query linear locally decodable codes over any field
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Short locally testable codes and proofs: a survey in two parts
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
Short locally testable codes and proofs
Studies in complexity and cryptography
SIAM Journal on Computing
Reliable computations based on locally decodable codes
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects 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
From irreducible representations to locally decodable codes
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Nearly private information retrieval
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Private locally decodable codes
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
New bounds for matching vector families
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
We prove that if a linear error-correcting code C:\{0,1\}^n\to\{0,1\}^m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2^{\Omega(n)}. We also present several extensions of this result.We show a reduction from the complexity of one-round, information-theoretic Private Information Retrieval Systems (with two servers) to Locally Decodable Codes, and conclude that if all the servers' answers are linear combinations of the database content, then t = \Omega(n/2^a), where t is the length of the user's query and a is the length of the servers' answers. Actually, 2^a can be replaced by O(a^k), where k is the number of bit locations in the answer that are actually inspected in the reconstruction.