Bias vs structure of polynomials in large fields, and applications in effective algebraic geometry and coding theory
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[1] Ming-Deh A. Huang,et al. An Algorithm for Approximate Counting of Points on Algebraic Sets over Finite Fields , 1998, ANTS.
[2] Ben Green,et al. The distribution of polynomials over finite fields, with applications to the Gowers norms , 2007, Contributions Discret. Math..
[3] Peter Elias,et al. List decoding for noisy channels , 1957 .
[4] Eyal Kushilevitz,et al. Learning decision trees using the Fourier spectrum , 1991, STOC '91.
[5] Grete Hermann,et al. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale , 1926 .
[6] Leonid A. Levin,et al. A hard-core predicate for all one-way functions , 1989, STOC '89.
[7] Andrej Bogdanov. Pseudorandom generators for low degree polynomials , 2005, STOC '05.
[8] Christopher Umans,et al. Simple extractors for all min-entropies and a new pseudorandom generator , 2005, JACM.
[9] Leonard M. Adleman,et al. Counting Rational Points on Curves and Abelian Varieties over Finite Fields , 1996, ANTS.
[10] Luca Trevisan,et al. List-decoding using the XOR lemma , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..
[11] Abhishek Bhowmick,et al. Using higher-order Fourier analysis over general fields , 2015, Electron. Colloquium Comput. Complex..
[12] Parikshit Gopalan,et al. A Fourier-Analytic Approach to Reed–Muller Decoding , 2010, IEEE Transactions on Information Theory.
[13] Selmer M. Johnson. A new upper bound for error-correcting codes , 1962, IRE Trans. Inf. Theory.
[14] Madhu Sudan,et al. Decodability of group homomorphisms beyond the johnson bound , 2008, STOC '08.
[15] Ronitt Rubinfeld,et al. Learning polynomials with queries: The highly noisy case , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.
[16] Jeffrey C. Jackson,et al. An efficient membership-query algorithm for learning DNF with respect to the uniform distribution , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.
[17] Emanuele Viola. The Sum of d Small-Bias Generators Fools Polynomials of Degree d , 2008, Computational Complexity Conference.
[18] Ming-Deh A. Huang,et al. Counting rational points on curves over finite fields , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.
[19] Sergey Yekhanin,et al. Detecting Rational Points on Hypersurfaces over Finite Fields , 2008, 2008 23rd Annual IEEE Conference on Computational Complexity.
[20] Arnab Bhattacharyya. Polynomial Decompositions in Polynomial Time , 2014, ESA.
[21] Parikshit Gopalan. A Fourier-Analytic Approach to Reed-Muller Decoding , 2013, IEEE Trans. Inf. Theory.
[22] Madhur Tulsiani,et al. Algorithmic regularity for polynomials and applications , 2013, SODA.
[23] Emanuele Viola,et al. Pseudorandom Bits for Polynomials , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).
[24] Venkatesan Guruswami,et al. Algorithms for Modular Counting of Roots of Multivariate Polynomials , 2006, Algorithmica.
[25] Marek Karpinski,et al. Counting curves and their projections , 1993, computational complexity.
[26] E. Szemerédi. Regular Partitions of Graphs , 1975 .
[27] W. Brownawell. Bounds for the degrees in the Nullstellensatz , 1987 .
[28] Shachar Lovett. Holes in Generalized Reed–Muller Codes , 2010, IEEE Transactions on Information Theory.
[29] Vladimir M. Blinovsky,et al. List decoding , 1992, Discret. Math..
[30] Amnon Ta-Shma,et al. Extractors from Reed-Muller Codes , 2001, Electron. Colloquium Comput. Complex..
[31] Shachar Lovett,et al. Every locally characterized affine-invariant property is testable , 2013, STOC '13.
[32] Shulim Kaliman,et al. On a theorem of Ax , 2004 .
[33] J. Kollár. Sharp effective Nullstellensatz , 1988 .
[34] Shafi Goldwasser,et al. Proving hard-core predicates using list decoding , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..
[35] Luca Trevisan,et al. Pseudorandom generators without the XOR lemma , 1999, Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317).
[36] Enkatesan G Uruswami. Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes , 2008 .
[37] Terence Tao,et al. Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets , 2012, Contributions Discret. Math..
[38] Alan M. Frieze,et al. Quick Approximation to Matrices and Applications , 1999, Comb..
[39] Shachar Lovett,et al. Worst Case to Average Case Reductions for Polynomials , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.