@article{6d860493ed954a21808c34b5cfb8e447,
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",
author = "Irit Dinur and Shai Evra and Ron Livne and Alexander Lubotzky and Shahar Mozes",
note = "We wish to thank Prahladh Harsha and Avi Wigderson for many interesting discussions along the way of this project. We thank Tali Kaufman for her in influential role in connecting LTCs and high dimensional expansion. We thank Yakov Varshavsky who gave upon our request a semester-long course describing the theory of p-adic uniformization (see Section 5). This work started by the first and fourth authors during a year long program at the Israeli Institute of Advanced Studies (IIAS) on high dimensional expanders in 2017. It was presented by the first author on October 6, 2021, at the Simons Institute for the Theory of Computing [25] as part of the lecture series on breakthroughs in computer science, and at the Institute for Advanced Study in Princeton on October 25-26, 2021 [26]. It was also presented by the fourth author on October 27, 2021 at the Simon{\textquoteright}s HDX21 workshop [53]. The authors are very grateful to these institutions and for the remarks of the audience which improved the exposition of the paper. Irit Dinur acknowledges support by ERC grant 772839 and ISF grant 2073/21. Shai Evra is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship. Alexander Lubotzky{\textquoteright}s research is supported by the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement No 882751). Shahar Mozes acknowledges support by ISF-Moked grant 2019/19. The first, second and forth authors are indebted to support from the IAS, Princeton",
year = "2022",
month = jul,
day = "25",
doi = "https://doi.org/10.48550/arXiv.2207.11929",
language = "الإنجليزيّة",
}