High Dimensional Expansion Implies Amplified Local Testability

Tali Kaufman, Izhar Oppenheim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022
EditorsAmit Chakrabarti, Chaitanya Swamy
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772495
DOIs
StatePublished - 1 Sep 2022
Event25th 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 202221 Sep 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume245
ISSN (Print)1868-8969

Conference

Conference25th International Conference on Approximation Algorithms for Combinatorial Optimization Problems and the 26th International Conference on Randomization and Computation, APPROX/RANDOM 2022
Country/TerritoryUnited States
CityVirtual, Urbana-Champaign
Period19/09/2221/09/22

Keywords

  • Amplified testing
  • High dimensional expanders
  • Locally testable codes

ASJC Scopus subject areas

  • Software

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