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
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
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
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
Towards 3-query locally decodable codes of subexponential length
Journal of the ACM (JACM)
Locally decodable codes and private information retrieval schemes
Locally decodable codes and private information retrieval schemes
Corruption and Recovery-Efficient Locally Decodable Codes
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
On Matrix Rigidity and Locally Self-Correctable Codes
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
New bounds for matching vector families
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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A linear (q,δ, ε, m(n))-locally decodable code (LDC) C: Fn → Fm(n) is a linear transformation from the vector space Fn to the space Fm(n) for which each message symbol xi can be recovered with probability at least 1/|F| + ε from C(x) by a randomized algorithm that queries only q positions of C(x), even if up to δm(n) positions of C(x) are corrupted. In a recent work of Dvir, the author shows that lower bounds for linear LDCs can imply lower bounds for arithmetic circuits. He suggests that proving lower bounds for LDCs over the complex or real field is a good starting point for approaching one of his conjectures. Our main result is anm(n) = Ω(n2) lower bound for linear 3-query LDCs over any, possibly infinite, field. The constant in the Ω(ċ) depends only on ε and δ. This is the first lower bound better than the trivial m(n) = Ω(n) for arbitrary fields and more than two queries.