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Electronic Colloquium on Computational Complexity

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All reports by Author Dan Carmon:

TR21-103 | 18th July 2021
Eli Ben-Sasson, Dan Carmon, Swastik Kopparty, David Levit

Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields

Over finite fields $F_q$ containing a root of unity of smooth order $n$ (smoothness means $n$ is the product of small primes), the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division, interpolation and multi-point evaluation. These operations can ... more >>>

TR20-083 | 30th May 2020
Eli Ben-Sasson, Dan Carmon, Yuval Ishai, Swastik Kopparty, Shubhangi Saraf

Proximity Gaps for Reed-Solomon Codes

Revisions: 3

A collection of sets displays a proximity gap with respect to some property if for every set in the collection, either (i) all members are $\delta$-close to the property in relative Hamming distance or (ii) only a tiny fraction of members are $\delta$-close to the property. In particular, no set ... more >>>

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