A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log n + O(1) additional random bits for sources with constant entropy rate. We further construct dispersers, which are similar to one-sided extractors, ... 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 >>>

We give the first explicit construction of deterministic extractors for affine sources over $F_2$, with entropy $k \geq \log^C n$ for some large enough constant $C$, where $n$ is the length of the source. Previously the best known results are by Bourgain \cite{Bourgain07}, Yehudayoff \cite{Yehudayoff10} and Li \cite{Li11a}, which require ... more >>>