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STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The probabilistic method yields deterministic parallel algorithms
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Some structural properties of low-rank matrices related to computational complexity
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Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Pseudorandom generators for low degree polynomials
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Constructions of Low-Degree and Error-Correcting \in-Biased Generators
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Testing k-wise and almost k-wise independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Pseudorandom Bits for Polynomials
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Inverse conjecture for the gowers norm is false
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Sum of d Small-Bias Generators Fools Polynomials of Degree d
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Noisy Interpolating Sets for Low Degree Polynomials
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Perturbed identity matrices have high rank: Proof and applications
Combinatorics, Probability and Computing
Random Low Degree Polynomials are Hard to Approximate
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
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A distribution Don a set $S \subset \mathbb Z_{p}^{N}$ 茂戮驴-fools polynomials of degree at most din Nvariables over $\mathbb Z_{p}$ if for any such polynomial P, the distribution of P(x) when xis chosen according to Ddiffers from the distribution when xis chosen uniformly by at most 茂戮驴in the 茂戮驴1norm. Distributions of this type generalize the notion of 茂戮驴-biased spaces and have been studied in several recent papers. We establish tight bounds on the minimum possible size of the support Sof such a distribution, showing that any such Ssatisfies $$ |S|\geq c_{1} \cdot \left(\frac{(\frac{N}{2d})^{d} \cdot \log{p}}{\epsilon^{2}\log{(\frac{1}{\epsilon})}}+p\right). $$This is nearly optimal as there is such an Sof size at most $$ c_{2} \cdot \frac{(\frac{3N}{d})^{d} \cdot \log{p} + p}{\epsilon^{2}}. $$