Abstract
Error-correcting codes and related combinatorial constructs play an important role is several recent (and old) results in complexity theory. This course will give a brief overview of the theory, constructions, algorithms, and applications of error-correcting codes. We will begin with basic definitions and the constructions of Reed-Solomon, Reed-Muller, and low-weight parity-check codes, then see unique-decoding and list-decoding algorithms, and finally, as time allows, applications to secret-sharing, hashing, private information retrieval, average-case complexity and probabilistically checkable proofs.
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© 2003 Springer-Verlag Berlin Heidelberg
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Trevisan, L. (2003). Error-Correcting Codes in Complexity Theory. In: Petreschi, R., Persiano, G., Silvestri, R. (eds) Algorithms and Complexity. CIAC 2003. Lecture Notes in Computer Science, vol 2653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44849-7_4
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DOI: https://doi.org/10.1007/3-540-44849-7_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40176-6
Online ISBN: 978-3-540-44849-5
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