Good Locally Testable Codes

Irit Dinur; Shai Evra; Ron Livne; Alexander Lubotzky; Shahar Mozes

doi:10.4007/annals.2026.203.2.3

Good Locally Testable Codes

Weizmann Institute of Science, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the c³-problem.

Original language	English
Pages (from-to)	511-553
Number of pages	43
Journal	Annals of Mathematics
Volume	203
Issue number	2
DOIs	https://doi.org/10.4007/annals.2026.203.2.3
State	Published - Mar 2026

Keywords

error correcting codes
left right Cayley complex
local testability
locally testable codes

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.4007/annals.2026.203.2.3

https://arxiv.org/abs/2207.11929License: CC BY

Cite this

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title = "Good Locally Testable Codes",

abstract = "An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the c3-problem.",

keywords = "error correcting codes, left right Cayley complex, local testability, locally testable codes",

author = "Irit Dinur and Shai Evra and Ron Livne and Alexander Lubotzky and Shahar Mozes",

note = "Publisher Copyright: {\textcopyright} 2026 Department of Mathematics, Princeton University.",

year = "2026",

month = mar,

doi = "10.4007/annals.2026.203.2.3",

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T1 - Good Locally Testable Codes

AU - Dinur, Irit

AU - Evra, Shai

AU - Livne, Ron

AU - Lubotzky, Alexander

AU - Mozes, Shahar

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N2 - An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the c3-problem.

AB - An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the c3-problem.

KW - error correcting codes

KW - left right Cayley complex

KW - local testability

KW - locally testable codes

UR - https://www.scopus.com/pages/publications/105032132334

U2 - 10.4007/annals.2026.203.2.3

DO - 10.4007/annals.2026.203.2.3

M3 - Article

SN - 0003-486X

VL - 203

SP - 511

EP - 553

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -

Good Locally Testable Codes

Abstract

Keywords

ASJC Scopus subject areas

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