Amir Shpilka

In this work we give two new constructions of $\epsilon$-biased

generators. Our first construction answers an open question of

Dodis and Smith, and our second construction

significantly extends a result of Mossel et al.

In particular we obtain the following results:

1. We construct a family of asymptotically good binary ... more >>>

Scott Aaronson, Travis Hance

Around 2002, Leonid Gurvits gave a striking randomized algorithm to approximate the permanent of an n×n matrix A. The algorithm runs in O(n^2/?^2) time, and approximates Per(A) to within ±?||A||^n additive error. A major advantage of Gurvits's algorithm is that it works for arbitrary matrices, not just for nonnegative matrices. ... more >>>

Silas Richelson, Sourya Roy

Random walks in expander graphs and their various derandomizations (e.g., replacement/zigzag product) are invaluable tools from pseudorandomness. Recently, Ta-Shma used s-wide replacement walks in his breakthrough construction of a binary linear code almost matching the Gilbert-Varshamov bound (STOC 2017). Ta-Shma’s original analysis was entirely linear algebraic, and subsequent developments have ... more >>>

Guy Blanc, Dean Doron

We construct a family of binary codes of relative distance $\frac{1}{2}-\varepsilon$ and rate $\varepsilon^{2} \cdot 2^{-\log^{\alpha}(1/\varepsilon)}$ for $\alpha \approx \frac{1}{2}$ that are decodable, probabilistically, in near linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who ... more >>>