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All reports by Author Yoav Tzur:

TR09-088 | 29th September 2009
Shachar Lovett, Yoav Tzur

Explicit lower bound for fooling polynomials by the sum of small-bias generators

Recently, Viola (CCC'08) showed that the sum of $d$ small-biased distributions fools degree-$d$ polynomial tests; that is, every polynomial expression of degree at most $d$ in the bits of the sum has distribution very close to that induced by this expression evaluated on uniformly selected random bits. We show that ... more >>>

TR09-018 | 8th March 2009
Yoav Tzur

$GF(2^n)$-Linear Tests versus $GF(2)$-Linear Tests

Comments: 1

A small-biased distribution of bit sequences is defined as one withstanding $GF(2)$-linear tests for randomness, which are linear combinations of the bits themselves. We consider linear combinations over larger fields, specifically, $GF(2^n)$ for $n$ that divides the length of the bit sequence. Indeed, this means that we partition the bits ... more >>>

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