We consider the problem of bit extraction from independent sources. We
construct an extractor that can extract from a constant number of
independent sources of length n, each of which have min-entropy
n^\gamma for an arbitrarily small constant \gamma > 0. Our
constructions are different from recent extractor constructions
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A code \mathcal{C} is (1-\tau,L) erasure list-decodable if for every codeword w, after erasing any 1-\tau fraction of the symbols of w,
the remaining \tau-fraction of its symbols have at most L possible completions into codewords of \mathcal{C}.
Non-explicitly, there exist binary (1-\tau,L) erasure list-decodable codes having rate O(\tau) and ... more >>>

A long line of work in the past two decades or so established close connections between several different pseudorandom objects and applications, including seeded or seedless non-malleable extractors, two source extractors, (bipartite) Ramsey graphs, privacy amplification protocols with an active adversary, non-malleable codes and many more. These connections essentially show ... more >>>