Oded Goldreich, Avishay Tal

We prove that random $n$-by-$n$ Toeplitz (alternatively Hankel) matrices over $GF(2)$ have rigidity $\Omega(\frac{n^3}{r^2\log n})$ for rank $r \ge \sqrt{n}$, with high probability. This improves, for $r = o(n/\log n \log\log n)$, over the $\Omega(\frac{n^2}{r} \cdot\log(\frac{n}{r}))$ bound that is known for many explicit matrices.

Our result implies that the explicit ... more >>>

Oded Goldreich

We consider arithmetic circuits with arbitrary large (multi-linear) gates for computing multi-linear functions. An adequate complexity measure for such circuits is the maximum between the arity of the gates and their number.

This model and the corresponding complexity measure were introduced by Goldreich and Wigderson (ECCC, TR13-043, 2013), ...
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