High Dimensional Expansion Implies Amplified Local Testability

Tali Kaufman; Izhar Oppenheim

doi:10.4230/LIPIcs.APPROX/RANDOM.2022.5

High Dimensional Expansion Implies Amplified Local Testability

Tali Kaufman, Izhar Oppenheim

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this work, we define a notion of local testability of codes that is strictly stronger than the basic one (studied e.g., by recent works on high rate LTCs), and we term it amplified local testability. Amplified local testability is a notion close to the result of optimal testing for Reed-Muller codes achieved by Bhattacharyya et al. We present a scheme to get amplified locally testable codes from high dimensional expanders. We show that single orbit Affine invariant codes, and in particular Reed-Muller codes, can be described via our scheme, and hence are amplified locally testable. This gives the strongest currently known testability result of single orbit affine invariant codes, strengthening the celebrated result of Kaufman and Sudan.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022
Editors	Amit Chakrabarti, Chaitanya Swamy
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959772495
DOIs	https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.5
State	Published - 1 Sep 2022
Event	25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022 - Virtual, Urbana-Champaign, United States Duration: 19 Sep 2022 → 21 Sep 2022

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	245
ISSN (Print)	1868-8969

Conference

Conference	25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022
Country/Territory	United States
City	Virtual, Urbana-Champaign
Period	19/09/22 → 21/09/22

Bibliographical note

Publisher Copyright:
© Tali Kaufman and Izhar Oppenheim.

Funding

Funding Tali Kaufman: This work was partially funded by ERC grant no. 336283 and BSF grant no. 2012256. Izhar Oppenheim: This work was partially funded by ISF grant no. 293/18.

Funders	Funder number
European Commission	336283
United States-Israel Binational Science Foundation	2012256
Israel Science Foundation	293/18

Keywords

Amplified testing
High dimensional expanders
Locally testable codes

Access to Document

10.4230/LIPIcs.APPROX/RANDOM.2022.5

Cite this

Kaufman, T., & Oppenheim, I. (2022). High Dimensional Expansion Implies Amplified Local Testability. In A. Chakrabarti, & C. Swamy (Eds.), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022 Article 5 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 245). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.5

Kaufman, Tali ; Oppenheim, Izhar. / High Dimensional Expansion Implies Amplified Local Testability. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022. editor / Amit Chakrabarti ; Chaitanya Swamy. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. (Leibniz International Proceedings in Informatics, LIPIcs).

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Kaufman, T & Oppenheim, I 2022, High Dimensional Expansion Implies Amplified Local Testability. in A Chakrabarti & C Swamy (eds), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022., 5, Leibniz International Proceedings in Informatics, LIPIcs, vol. 245, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022, Virtual, Urbana-Champaign, United States, 19/09/22. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.5

High Dimensional Expansion Implies Amplified Local Testability. / Kaufman, Tali; Oppenheim, Izhar.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022. ed. / Amit Chakrabarti; Chaitanya Swamy. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. 5 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 245).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Kaufman T, Oppenheim I. High Dimensional Expansion Implies Amplified Local Testability. In Chakrabarti A, Swamy C, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2022. 5. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.APPROX/RANDOM.2022.5

High Dimensional Expansion Implies Amplified Local Testability

Abstract

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Bibliographical note

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Keywords

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