Fetching the paper…
Reading the bibliography…
A locally testable code (LTC) is an error-correcting code that has a property-tester.
The Theory of Groups, vol. 2
Aleksandr Gennadievich Kurosh · 1955
Earlier work this paper cites.
Low density parity check codes
Robert G. Gallager · 1963
Earlier work this paper cites.
p-adic curvature and the cohomology of discrete subgroups of p-adic groups
Howard Garland · 1973
Earlier work this paper cites.
An algebraic surface with k ample, ( K 2 ) = 9 , p g = q = 0 ({K}^{2})=9,p_{g}=q=0
David Mumford · 1979
Earlier work this paper cites.
A recursive approach to low complexity codes
R. Michael Tanner · 1981
Earlier work this paper cites.
Explicit construction of linear sized tolerant networks
Noga Alon and Fan RK Chung · 1988
Earlier work this paper cites.
Ramanujan graphs
Alexander Lubotzky, Ralph Phillips, and Peter Sarnak · 1988
Earlier work this paper cites.
Self-testing/correcting with applications to numerical problems
Manuel Blum, Michael Luby, and Ronitt Rubinfeld · 1990
Earlier work this paper cites.
Non-deterministic exponential time has two-prover interactive protocols
László Babai, Lance Fortnow, and Carsten Lund · 1991
Earlier work this paper cites.
Checking computations in polylogarithmic time
László Babai, Lance Fortnow, Leonid Levin, and Mario Szegedy · 1991
Earlier work this paper cites.
A zero entropy, mixing of all orders tiling system, symbolic dynamics and its applications
Shahar Mozes · 1991
Earlier work this paper cites.
Algebraic methods for interactive proof systems
Carsten Lund, Lance Fortnow, Howard Karloff, and Noam Nisan · 1992
Earlier work this paper cites.
Probabilistic checking of proofs and the hardness of approximation problems
Sanjeev Arora · 1994
Earlier work this paper cites.
Discrete groups, expanding graphs and invariant measures
Alexander Lubotzky · 1994
Earlier work this paper cites.
Existence and explicit constructions of q + 1 q+1 regular Ramanujan graphs for every prime power q q
Moshe Morgenstern · 1994
Earlier work this paper cites.
Nearly linear size holographic proofs
Alexander Polishchuk and Dan Spielman · 1994
Earlier work this paper cites.
Robust characterizations of polynomials with applications to program testing
Ronitt Rubinfeld and Madhu Sudan · 1996
Earlier work this paper cites.
Linear-time encodable and decodable error-correcting codes
Daniel A. Spielman · 1996
Earlier work this paper cites.
Expander codes
Michael Sipser and Daniel A. Spielman · 1996
Earlier work this paper cites.
Proof verification and intractability of approximation problems
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy · 1998
Earlier work this paper cites.
Probabilistic checking of proofs: A new characterization of NP
Sanjeev Arora and Shmuel Safra · 1998
Earlier work this paper cites.
A family of A ~ n \tilde{A}_{n} -groups
Donald I. Cartwright and Tim Steger · 1998
Earlier work this paper cites.
p-adic uniformization of unitary Shimura varieties
Yakov Varshavsky · 1998
Cited alongside, same era.
The Ramanujan property for regular cubical complexes
Bruce Jordan and Ron Livne · 1999
Cited alongside, same era.
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Eli Ben-Sasson, Madhu Sudan, Salil P. Vadhan, and Avi Wigderson · 2003
Cited alongside, same era.
Some 3CNF properties are hard to test
Eli Ben-Sasson, Prahladh Harsha, and Sofya Raskhodnikova · 2005
Cited alongside, same era.
Simple PCPs with poly-log rate and query complexity
Eli Ben-Sasson and Madhu Sudan · 2005
Cited alongside, same era.
Locally testable cyclic codes
László Babai, Amir Shpilka, and Daniel Stefankovic · 2005
Cited alongside, same era.
Dense locally testable codes cannot have constant rate and distance
Irit Dinur and Tali Kaufman · 2011
Later among the works it cites.
Towards lower bounds on locally testable codes via density arguments
Eli Ben-Sasson and Michael Viderman · 2012
Later among the works it cites.
The tensor product of two good codes is not necessarily robustly testable
Oded Goldreich and Or Meir · 2012
Later among the works it cites.
Edge transitive Ramanujan graphs and symmetric LDPC good codes
Tali Kaufman and Alexander Lubotzky · 2012
Later among the works it cites.
Some improvements to total degree tests
Katalin Friedl and Madhu Sudan · 2013
Later among the works it cites.
Ramanujan complexes and bounded degree topological expanders
Tali Kaufman, David Kazhdan, and Alexander Lubotzky · 2014
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Short locally testable codes and proofs (survey)
Oded Goldreich · 2005
Cited alongside, same era.
Ramanujan complexes of type A d ~ \tilde{A_{d}}
Alexander Lubotzky, Beth Samuels, and Uzi Vishne · 2005
Cited alongside, same era.
Explicit constructions of Ramanujan complexes of type A d ~ \tilde{A_{d}}
Alexander Lubotzky, Beth Samuels, and Uzi Vishne · 2005
Cited alongside, same era.
The tensor product of two codes is not necessarily robustly testable
Paul Valiant · 2005
Cited alongside, same era.
Robust PCPs of proximity, shorter PCPs and applications to coding
Eli Ben-Sasson, Oded Goldreich, Prahladh Harsha, Madhu Sudan, and Salil Vadhan · 2006
Cited alongside, same era.
Robust locally testable codes and products of codes
Eli Ben-Sasson and Madhu Sudan · 2006
Cited alongside, same era.
Later among the works it cites.
High dimensional expanders and property testing
Tali Kaufman and Alexander Lubotzky · 2014
Later among the works it cites.
Bounded degree cosystolic expanders of every dimension
Shai Evra and Tali Kaufman · 2016
Later among the works it cites.
Agreement expansion
Irit Dinur and Tali Kaufman · 2017
Later among the works it cites.
Introduction to Property Testing
Oded Goldreich · 2017
Later among the works it cites.
High-rate locally correctable and locally testable codes with sub-polynomial query complexity
Swastik Kopparty, Or Meir, Noga Ron-Zewi, and Shubhangi Saraf · 2017
Later among the works it cites.
Boolean function analysis on high-dimensional expanders
Yotam Dikstein, Irit Dinur, Yuval Filmus, and Prahladh Harsha · 2018
Later among the works it cites.
Locally testable and locally correctable codes approaching the gilbert-varshamov bound
Sivakanth Gopi, Swastik Kopparty, Rafael Mendes de Oliveira, Noga Ron-Zewi, and Shubhangi Saraf · 2018
Later among the works it cites.
Local spectral expansion approach to high dimensional expanders part I: descent of spectral gaps
Izhar Oppenheim · 2018
Later among the works it cites.
Log-concave polynomials ii: high-dimensional walks and an fpras for counting bases of a matroid
Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant · 2019
Later among the works it cites.
Balanced product quantum codes
Nikolas P. Breuckmann and Jens N. Eberhardt · 2021
Closest in time.
Breakthroughs in computer science: Locally testable codes with constant rate, distance, and locality
Irit Dinur · 2021
Closest in time.
Locally testable codes with constant rate, distance, and locality
Irit Dinur · 2021
Closest in time.
The c 3 c^{3} problem: Locally testable codes with constant rate and constant distance
Alexander Lubotzky · 2021
Closest in time.
Quantum LDPC codes with almost linear minimum distance
Pavel Panteleev and Gleb Kalachev · 2021
Closest in time.
Asymptotically good quantum and locally testable classical LDPC codes, 2021
Pavel Panteleev and Gleb Kalachev · 2021
Closest in time.