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Electronic Colloquium on Computational Complexity

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All reports by Author Amnon Ta-Shma:

TR22-078 | 8th May 2022
Dan Karliner, Amnon Ta-Shma

Improved local testing for multiplicity codes

Multiplicity codes are a generalization of Reed-Muller codes which include derivatives as well as the values of low degree polynomials, evaluated in every point in $\mathbb{F}_p^m$.
Similarly to Reed-Muller codes, multiplicity codes have a local nature that allows for local correction and local testing.
Recently, the authors and ... more >>>

TR22-073 | 18th May 2022
Itay Kalev, Amnon Ta-Shma

Unbalanced Expanders from Multiplicity Codes

In 2007 Guruswami, Umans and Vadhan gave an explicit construction of a lossless condenser based on Parvaresh-Vardy codes. This lossless condenser is a basic building block in many constructions, and, in particular, is behind the state of the art extractor constructions.

We give an alternative construction that is based on ... more >>>

TR22-028 | 23rd February 2022
Dan Karliner, Roie Salama, Amnon Ta-Shma

The plane test is a local tester for Multiplicity Codes

Multiplicity codes are a generalization of RS and RM codes where for each evaluation point we output the evaluation of a low-degree polynomial and all of its directional derivatives up to order $s$. Multi-variate multiplicity codes are locally decodable with the natural local decoding algorithm that reads values on a ... more >>>

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