An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Extractors and lower bounds for locally samplable sources
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Capacity achieving two-write WOM codes
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Improving the Hadamard extractor
Theoretical Computer Science
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We give polynomial time computable extractors for \emph{low-weight affince sources}. A distribution is affine if it samples a randompoints from some unknown low dimensional subspace of $\mathbb{F}_2^n$. A distribution is low weight affine if the corresponding linear spacehas a basis of low-weight vectors. Low-weight affine sources are thus a generalization of the well studied models of bit-fixing sources (which are just weight $1$ affine sources). For universal constants $c,\epsilon$, our extractors can extract almost allthe entropy from weight $k^{\epsilon}$ affine sources of dimension $k$, as long as $k \log ^c n$, with error $2^{-k^{\Omega(1)}}$. In particular, our results give new extractors for low entropy bit-fixing sources, with exponentially small error, a parameter that is important for the application of these extractors to cryptography. Our techniques involve constructing new \emph{condensers} for \emph{affine somewhere random sources}.