  We construct a pseudorandom generator which fools read-$k$ oblivious
branching programs and, more generally, any linear length oblivious branching
program, assuming that the sequence according to which the bits are read is
known in advance. For polynomial width branching programs, the seed lengths in
our constructions are $\tilde{O}(n^{1-1/2^{k-1}})$ (for the read-$k$ case) and
$O(n/ \log \log n)$ (for the linear length case). Previously, the best
construction for these models required seed length $(1-\Omega(1))n$.
