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Higher-order Fourier analysis, developed over prime fields, has been recently used in different areas of computer science, including list decoding, algorithmic decomposition and testing.
Über ein problem aus dem gebiete der diophantischen approximationen
Hermann Weyl · 1914
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List decoding for noisy channels
P. Elias · 1957
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List decoding
J. Wozencraft · 1958
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Schnelle multiplikation grosser zahlen
Arnold Schönhage and Volker Strassen · 1971
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Random walks arising in random number generation
Fan R. K. Chung, Persi Diaconis, and Ronald L. Graham · 1987
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The influence of variables on boolean functions
Jeff Kahn, Gil Kalai, and Nathan Linial · 1988
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A hard-core predicate for all one-way functions
O. Goldreich and L. Levin · 1989
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Non-deterministic exponential time has two-prover interactive protocols
László Babai, Lance Fortnow, and Carsten Lund · 1991
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Checking computations in polylogarithmic time
László Babai, Lance Fortnow, Leonid A. Levin, and Mario Szegedy · 1991
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Self-testing/correcting with applications to numerical problems
Manuel Blum, Michael Luby, and Ronitt Rubinfeld · 1993
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Constructing small sample spaces satisfying given constraints
D. Koller and N. Megiddo · 1993
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Learning decision trees using the Fourier spectrum
E. Kushilevitz and Y. Mansour · 1993
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Small-bias probability spaces: efficient constructions and applications
Joseph Naor and Moni Naor · 1993
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Interactive proofs and the hardness of approximating cliques
Uriel Feige, Shafi Goldwasser, László Lovász, Shmuel Safra, and Mario Szegedy · 1996
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Robust characterizations of polynomials with applications to program testing
Ronitt Rubinfeld and Madhu Sudan · 1996
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An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
J. Jackson · 1997
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Decoding of Reed-Solomon codes beyond the error-correction bound
M. Sudan · 1997
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Property testing and its connection to learning and approximation
Oded Goldreich, Shafi Goldwasser, and Dana Ron · 1998
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A new proof of Szeméredi’s theorem for arithmetic progressions of length four
William T. Gowers · 1998
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Learning polynomials with queries: The highly noisy case
O. Goldreich, R. Rubinfeld, and M. Sudan · 2000
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Fourier transform in computer science
Daniel Štefankovič · 2000
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List decoding: Algorithms and applications
M. Sudan · 2000
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A new proof of Szeméredi’s theorem
William T. Gowers · 2001
Earlier work this paper cites.
Some optimal inapproximability results
Johan Hastad · 2001
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Pseudorandom generators without the XOR lemma
M. Sudan, L. Trevisan, and S. P. Vadhan · 2001
Cited alongside, same era.
Extractors from Reed-Muller codes
A. Ta-Shma, D. Zuckerman, and S. Safra · 2001
Cited alongside, same era.
Proving hard-core predicates using list decoding
A. Akavia, S. Goldwasser, and S. Safra · 2003
Cited alongside, same era.
Improved low-degree testing and its applications
S. Arora and M. Sudan · 2003
Cited alongside, same era.
List-decoding using the XOR lemma
L. Trevisan · 2003
Cited alongside, same era.
List Decoding of Error-Correcting Codes
V. Guruswami · 2004
A unified framework for testing linear-invariant properties
Arnab Bhattacharyya, Elena Grigorescu, and Asaf Shapira · 2010
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An inverse theorem for the uniformity seminorms associated with the action of 𝔽 ω {{\mathbb{F}}}^{\omega}
Vitaly Bergelson, Terence Tao, and Tamar Ziegler · 2010
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A Fourier-analytic approach to Reed-Muller decoding
P. Gopalan · 2010
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Linear equations in primes
Ben Green and Terence Tao · 2010
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Noise stability of functions with low influences: Invariance and optimality
Elchanan Mossel, Ryan O’Donnell, and Krzysztof Oleszkiewicz · 2010
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The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
Terence Tao and Tamar Ziegler · 2010
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Cited alongside, same era.
List decoding of q-ary Reed-Muller codes
R. Pellikaan and X. Wu · 2004
Cited alongside, same era.
Testing Reed-Muller codes
Noga Alon, Tali Kaufman, Michael Krivelevich, Simon Litsyn, and Dana Ron · 2005
Cited alongside, same era.
Finite field models in additive combinatorics
Ben Green · 2005
Cited alongside, same era.
Nonconventional ergodic averages and nilmanifolds
Bernard Host and Bryna Kra · 2005
Cited alongside, same era.
Almost orthogonal linear codes are locally testable
Tali Kaufman and Simon Litsyn · 2005
Cited alongside, same era.
Later among the works it cites.
Testing linear-invariant non-linear properties
Arnab Bhattacharyya, Victor Chen, Madhu Sudan, and Ning Xie · 2011
Later among the works it cites.
Symmetric LDPC codes are not necessarily locally testable
Eli Ben-Sasson, Ghid Maatouk, Amir Shpilka, and Madhu Sudan · 2011
Later among the works it cites.
Proximity oblivious testing and the role of invariances
Oded Goldreich and Tali Kaufman · 2011
Later among the works it cites.
On proximity oblivious testing
Oded Goldreich and Dana Ron · 2011
Later among the works it cites.
An inverse theorem for the Gowers U 4 {U}^{4} -norm
Ben Green, Terence Tao, and Tamar Ziegler · 2011
Later among the works it cites.
Succinct representation of codes with applications to testing
Elena Grigorescu, Tali Kaufman, and Madhu Sudan · 2012
Later among the works it cites.
An inverse theorem for the Gowers U s + 1 {U}^{s+1} -norm
Ben Green, Terence Tao, and Tamar Ziegler · 2012
Later among the works it cites.
Higher Order Fourier Analysis
Terence Tao · 2012
Later among the works it cites.
The inverse conjecture for the Gowers norm over finite fields in low characteristic
Terence Tao and Tamar Ziegler · 2012
Later among the works it cites.
Pseudorandomness
Salil P. Vadhan · 2012
Later among the works it cites.
Every locally characterized affine-invariant property is testable
Arnab Bhattacharyya, Eldar Fischer, Hamed Hatami, Pooya Hatami, and Shachar Lovett · 2013
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Testing low complexity affine-invariant properties
Arnab Bhattacharyya, Eldar Fischer, and Shachar Lovett · 2013
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Estimating the distance from testable affine-invariant properties
Hamed Hatami and Shachar Lovett · 2013
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Polynomial decompositions in polynomial time
Arnab Bhattacharyya · 2014
Later among the works it cites.
List decoding Reed-Muller codes over small fields
Abhishek Bhowmick and Shachar Lovett · 2014
Later among the works it cites.
A characterization of locally testable affine-invariant properties via decomposition theorems
Yuichi Yoshida · 2014
Later among the works it cites.
Algorithmic regularity for polynomials and applications
Arnab Bhattacharyya, Pooya Hatami, and Madhur Tulsiani · 2015
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