All reports by Author Alexander Lubotzky:

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TR24-019
| 2nd February 2024
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Yotam Dikstein, Irit Dinur, Alexander Lubotzky#### Low Acceptance Agreement Tests via Bounded-Degree Symplectic HDXs

Revisions: 1

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TR21-151
| 8th November 2021
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Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, Shahar Mozes#### Locally Testable Codes with constant rate, distance, and locality

Revisions: 1

Yotam Dikstein, Irit Dinur, Alexander Lubotzky

We solve the derandomized direct product testing question in the low acceptance regime, by constructing new high dimensional expanders that have no small connected covers. We show that our complexes have swap cocycle expansion, which allows us to deduce the agreement theorem by relying on previous work.

Derandomized direct product ... more >>>

Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, Shahar Mozes

A locally testable code (LTC) is an error correcting code that has a property-tester. The tester reads $q$ bits that are randomly chosen, and rejects words with probability proportional to their distance from the code. The parameter $q$ is called the locality of the tester.

LTCs were initially studied as ... more >>>