Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
From affine to two-source extractors via approximate duality
Proceedings of the forty-third annual ACM symposium on Theory of computing
Linear-Algebraic List Decoding of Folded Reed-Solomon Codes
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
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
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
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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We construct explicit subspace-evasive sets. These are subsets of Fn of size |F|(1-ε)n whose intersection with any k-dimensional subspace is bounded by a constant c(k,ε). This problem was raised by Guruswami (CCC 2011) as it leads to optimal rate list-decodable codes of constant list size. The main technical ingredient is the construction of k low-degree polynomials whose common set of zeros has small intersection with any k-dimensional subspace.