In the {\em learning parities with noise} problem ---well-studied in learning theory and cryptography--- we
have access to an oracle that, each time we press a button,
returns a random vector $ a \in \GF(2)^n$ together with a bit $b \in \GF(2)$ that was computed as
$a\cdot u +\eta$, where ... more >>>

In this work we consider linear codes which are locally testable
in a sublinear number of queries. We give the first general family
of locally testable codes of exponential size. Previous results of
this form were known only for codes of quasi-polynomial size (e.g.
Reed-Muller codes). We accomplish this by ... more >>>

We study the problem of constructing affine extractors over $\mathsf{GF(2)}$. Previously the only known construction that can handle sources with arbitrarily linear entropy is due to Bourgain (and a slight modification by Yehudayoff), which relies heavily on the technique of Van der Corput differencing and a careful choice of a ... more >>>