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2021

High dimensional expansion implies amplified local testability

Kaufman, Tali, Oppenheim, Izhar

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In this work we show that high dimensional expansion implies locally testable code.

Specifically, we define a notion that we call high-dimensional-expanding-system (HDE-system).
This is a set system defined by incidence relations with certain high dimensional expansion relations between its sets.
We say that a linear code is modelled over HDE-system, if the collection of linear constraints that the code satisfies could by described via the HDE-system.

High dimensional expansion implies amplified local testability · Around

Built on

Algebraic property testing: the role of invariance
Tali Kaufman and Madhu Sudan · 2008
Earlier work this paper cites.
Optimal testing of Reed-Muller codes
Arnab Bhattacharyya, Swastik Kopparty, Grant Schoenebeck, Madhu Sudan, and David Zuckerman · 2010
Earlier work this paper cites.
Ramanujan complexes and bounded degree topological expanders
Tali Kaufman, David Kazhdan, and Alexander Lubotzky · 2014
Earlier work this paper cites.

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Then

High order random walks: beyond spectral gap
Tali Kaufman and Izhar Oppenheim · 2018
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Locally testable codes via high-dimensional expanders
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Yotam Dikstein, Irit Dinur, Prahladh Harsha, and Noga Ron-Zewi · 2020
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