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

Einstein Institute of Mathematics

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

Bibliographical note

Publisher Copyright:
© 2026 Department of Mathematics, Princeton University.

Keywords

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

Access to Document

10.4007/annals.2026.203.2.3

Cite this

@article{2f031a6a2f8f4cbf801ddaa37ac93651,

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",

language = "אנגלית",

volume = "203",

pages = "511--553",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Department of Mathematics at Princeton University",

number = "2",

}

TY - JOUR

T1 - Good Locally Testable Codes

AU - Dinur, Irit

AU - Evra, Shai

AU - Livne, Ron

AU - Lubotzky, Alexander

AU - Mozes, Shahar

PY - 2026/3

Y1 - 2026/3

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 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105032132334

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

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this