License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.5
URN: urn:nbn:de:0030-drops-171276
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17127/
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Kaufman, Tali ; Oppenheim, Izhar

High Dimensional Expansion Implies Amplified Local Testability

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LIPIcs-APPROX5.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{kaufman_et_al:LIPIcs.APPROX/RANDOM.2022.5,
  author =	{Kaufman, Tali and Oppenheim, Izhar},
  title =	{{High Dimensional Expansion Implies Amplified Local Testability}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{5:1--5:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17127},
  URN =		{urn:nbn:de:0030-drops-171276},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.5},
  annote =	{Keywords: Locally testable codes, High dimensional expanders, Amplified testing}
}

Keywords: Locally testable codes, High dimensional expanders, Amplified testing
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)
Issue Date: 2022
Date of publication: 15.09.2022

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