Chinese remaindering with errors
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A displacement approach to efficient decoding of algebraic-geometric codes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Oblivious transfer and polynomial evaluation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Pseudorandom generators without the XOR Lemma (extended abstract)
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Password hardening based on keystroke dynamics
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List decoding algorithms for certain concatenated codes
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Escrow services and incentives in peer-to-peer networks
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A Deterministic Multivariate Interpolation Algorithm for Small Finite Fields
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Journal of Intelligent Manufacturing
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Given an error-correcting code of block length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed-Solomon codes. The list decoding problem for Reed-Solomon codes reduces to the following ``curve-fitting'' problem over a field F: Given n points (x[i].y[i]), 1 1/3, where the result yields the first asymptotic improvement since Peterson's original algorithm nearly four decades ago.The algorithm generalizes to solve the list decoding problem for other algebraic codes, specifically alternant codes (a class of codes including BCH codes) and algebraic-geometric codes. In both cases, we obtain a list decoding algorithm that corrects up to n - sqrt{n(n-d')} errors, where n is the block length and d' is the designed distance of the code. The improvement for the case of algebraic-geometric codes extends the methods of Shokrollahi and Wasserman [STOC '98] and improves upon their bound for every choice of n and d'. We also present some other consequences of our algorithm including a solution to a weighted curve fitting problem, which is of use in soft-decision decoding algorithms for Reed-Solomon codes.