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For infinitely many rates $R \in (0,1)$, we show that full-length Reed-Solomon codes over fields of low characteristic can contain super-polynomially many codewords in a Hamming ball of radius just exceeding the Johnson radius. Over prime fields, we exhibit full-length Reed-Solomon codes of constant rate $R$ with polynomially many codewords ... more >>>
A quadratic source is a random variable $X\sim\mathbb{F}_2^n$ generated by applying $n$ quadratics to a hidden uniform string. Previously, the best-known explicit extractor for this model required min-entropy roughly $k=n-\sqrt{\log n}$. In this paper, we give an explicit construction for min-entropy $k=\mathrm{polylog}(n)$. Even for the special case of $2$-local sources, ... more >>>
We investigate the depth overhead of stretch-amplification for pseudorandom generators in the black-box model. We show that any black box construction of a PRG $H: \{0,1\}^m \to \{0,1\}^M$ which makes $\mathrm{poly}(n)$ queries to a PRG $G: \{0,1\}^n \to \{0,1\}^N$ in $d$ adaptive phases during each evaluation (and with a black-box ... more >>>
