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Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice.
Generalized Vandermonde Determinants and Roots of Unity of Prime Order
R. J. Evans and I. M. Isaacs · 1976
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Linear time erasure codes with nearly optimal recovery
Noga Alon, Jeff Edmonds, and Michael Luby · 1995
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Expander codes
M. Sipser and D.A. Spielman · 1996
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Improved decoding of Reed-Solomon and algebraic-geometric codes
V. Guruswami and M. Sudan · 1998
Earlier work this paper cites.
Expander-based constructions of efficiently decodable codes
V. Guruswami and P. Indyk · 2001
Earlier work this paper cites.
Near-optimal linear-time codes for unique decoding and new list-decodable codes over smaller alphabets
Venkatesan Guruswami and Piotr Indyk · 2002
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Linear time encodable and list decodable codes
Venkatesan Guruswami and Piotr Indyk · 2003
Earlier work this paper cites.
Simple proof of Chebotarev’s theorem on roots of unity, July 2004
P. E. Frenkel · 2004
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An uncertainty principle for cyclic groups of prime order, July 2004
Terence Tao · 2004
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Inequalities for Finite Group Permutation Modules
Daniel Goldstein, Robert M. Guralnick, and I. M. Isaacs · 2005
Earlier work this paper cites.
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
Venkatesan Guruswami and Atri Rudra · 2008
Earlier work this paper cites.
Quantum Computation and Quantum Information: 10th Anniversary Edition
Michael A. Nielsen and Isaac L. Chuang · 2010
Cited alongside, same era.
On the Locality of Codeword Symbols
Parikshit Gopalan, Cheng Huang, Huseyin Simitci, and Sergey Yekhanin · 2012
Cited alongside, same era.
Erasure Coding in Windows Azure Storage
Cheng Huang, Huseyin Simitci, Yikang Xu, Aaron Ogus, Brad Calder, Parikshit Gopalan, Jin Li, and Sergey Yekhanin · 2012
Cited alongside, same era.
Pseudorandomness
Salil P. Vadhan · 2012
Cited alongside, same era.
f4: Facebook’s Warm BLOB Storage System
Subramanian Muralidhar, Wyatt Lloyd, Sabyasachi Roy, Cory Hill, Ernest Lin, Weiwen Liu, Satadru Pan, Shiva Shankar, Viswanath Sivakumar, Linpeng Tang, and Sanjeev Kumar · 2014
Cited alongside, same era.
A Family of Optimal Locally Recoverable Codes
Itzhak Tamo and Alexander Barg · 2014
Cited alongside, same era.
On the Chebotarëv theorem over finite fields
Guanghui Zhang · 2019
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Local List Recovery of High-Rate Tensor Codes and Applications
Brett Hemenway, Noga Ron-Zewi, and Mary Wootters · 2020
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Explicit Near-Ramanujan Graphs of Every Degree
Sidhanth Mohanty, Ryan O’Donnell, and Pedro Paredes · 2021
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Circuit Lower Bounds for Low-Energy States of Quantum Code Hamiltonians
Anurag Anshu and Chinmay Nirkhe · 2022
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Approaching the Quantum Singleton Bound with Approximate Error Correction, December 2022
Thiago Bergamaschi, Louis Golowich, and Sam Gunn · 2022
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Locally testable codes with constant rate, distance, and locality
Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, and Shahar Mozes · 2022
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Explicit subspace designs
Venkatesan Guruswami and Swastik Kopparty · 2016
Cited alongside, same era.
High-rate locally-correctable and locally-testable codes with sub-polynomial query complexity
Swastik Kopparty, Or Meir, Noga Ron-Zewi, and Shubhangi Saraf · 2016
Cited alongside, same era.
Locally Testable and Locally Correctable Codes approaching the Gilbert-Varshamov Bound
Sivakanth Gopi, Swastik Kopparty, Rafael Oliveira, Noga Ron-Zewi, and Shubhangi Saraf · 2018
Cited alongside, same era.
Linear-time list recovery of high-rate expander codes
Brett Hemenway and Mary Wootters · 2018
Cited alongside, same era.
How Long Can Optimal Locally Repairable Codes Be?
Venkatesan Guruswami, Chaoping Xing, and Chen Yuan · 2019
Cited alongside, same era.
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Essential coding theory
Venkatesan Guruswami, Atri Rudra, and Madhu Sudan · 2022
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Quantum Tanner codes
Anthony Leverrier and Gilles Zémor · 2022
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Asymptotically good Quantum and locally testable classical LDPC codes
Pavel Panteleev and Gleb Kalachev · 2022
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Good Quantum LDPC Codes with Linear Time Decoders
Irit Dinur, Min-Hsiu Hsieh, Ting-Chun Lin, and Thomas Vidick · 2023
Closest in time.
Tradeoff Constructions for Quantum Locally Testable Codes, September 2023
Adam Wills, Ting-Chun Lin, and Min-Hsiu Hsieh · 2023
Closest in time.