Algorithmic results in list decoding
Foundations and Trends® in Theoretical Computer Science
Concatenated codes can achieve list-decoding capacity
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improvements on the Johnson bound for Reed-Solomon codes
Discrete Applied Mathematics
The existence of concatenated codes list-decodable up to the hamming bound
IEEE Transactions on Information Theory
Complexity of decoding positive-rate primitive Reed-Solomon codes
IEEE Transactions on Information Theory
Optimal rate list decoding via derivative codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In this paper, we prove the following two results that expose some combinatorial limitations to list decoding Reed-Solomon codes. 1) Given n distinct elements alpha1,...,alphan from a field F, and n subsets S1,...,Sn of F, each of size at most l, the list decoding algorithm of Guruswami and Sudan can in polynomial time output all polynomials p of degree at most k that satisfy p(alphai)isinSi for every i, as long as l