In this paper we prove two results about AC^0[\oplus] circuits.

We show that for d(N) = o(\sqrt{\log N/\log \log N}) and N \leq s(N) \leq 2^{dN^{1/d^2}} there is an explicit family of functions \{f_N:\{0,1\}^N\rightarrow \{0,1\}\} such that
f_N has uniform AC^0 formulas of depth d and size at ... more >>>