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
Upper Bound on Communication Complexity of Private Information Retrieval
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
General constructions for information-theoretic private information retrieval
Journal of Computer and System Sciences
Lower bounds for linear locally decodable codes and private information retrieval
Computational Complexity
Towards 3-query locally decodable codes of subexponential length
Journal of the ACM (JACM)
Locally Decodable Codes From Nice Subsets of Finite Fields and Prime Factors of Mersenne Numbers
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Communications of the ACM
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Testing non-uniform k-wise independent distributions over product spaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Locally testable vs. locally decodable codes
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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
Decoding frequency permutation arrays under Chebyshev distance
IEEE Transactions on Information Theory
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
Locally decodable codes: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Learning read-constant polynomials of constant degree modulo composites
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Short locally testable codes and proofs
Studies in complexity and cryptography
Limits on the rate of locally testable affine-invariant codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Public key locally decodable codes with short keys
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
SIAM Journal on Computing
Communication-efficient distributed oblivious transfer
Journal of Computer and System Sciences
A novel elementary construction of matching vectors
Information Processing Letters
From irreducible representations to locally decodable codes
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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
Local correctability of expander codes
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Locally Decodable Codes (LDC) allow one to decode any particular symbol of the input message by making a constant number of queries to a codeword, even if a constant fraction of the codeword is damaged. In a recent work [Yek08] Yekhanin constructs a 3-query LDC with sub-exponential length of size exp(exp(O((log n)/(log log n)))). However, this construction requires a conjecture that there are infinitely many Mersenne primes. In this paper we give the first unconditional constant query LDC construction with subexponantial codeword length. In addition our construction reduces codeword length. We give construction of 3-query LDC with codeword length exp(exp(O(√{log n log log n ))). Our construction could also be extended to higher number of queries. We give a 2r-query LDC with length of exp(exp(O(☂[r] log n (log log n)r-1))).