Some Applications of Coding Theory in Computational Complexity
<|reference_start|>Some Applications of Coding Theory in Computational Complexity: 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.<|reference_end|>
@article{trevisan2004some,
    title={Some Applications of Coding Theory in Computational Complexity},
    author={Luca Trevisan},
    journal={arXiv preprint arXiv:cs/0409044},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0409044},
    primaryClass={cs.CC cs.IT math.IT}
}