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Some Applications of Coding Theory in Computational Complexity
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Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs.
Forward citations
Cited by 2 Pith papers
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Improved Lower Bounds for all Odd-Query Locally Decodable Codes
For every odd q ≥ 3, any q-query binary locally decodable code with constant distance satisfies k ≤ O~(n^(1-2/q)), the first bound of this form for q ≥ 5.
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A $k^{\frac{q}{q-2}}$ Lower Bound for Odd Query Locally Decodable Codes from Bipartite Kikuchi Graphs
For every constant odd number of queries q, any q-query locally decodable code has length at least (k/(log k))^(q/(q-2)) up to constants.
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