  It is known that the automorphism group of the elementary abelian $2$-group
$Z_2^n$ is isomorphic to the general linear group $GL(n,F_2)$ of degree $n$
over $F_2$. Let $W$ be the collection of permutation matrices of order $n$. It
is clear that $W\le GL(n,F_2)$. In virtue of this, we consider the Cayley graph
$Cay(Z_2^n,S)$, where $S$ is the union of some orbits under the action of $W$.
We call such graphs the orbit Cayley graphs over $Z_2^n$. In this paper, we
give eight infinite families of strongly regular graphs among orbit Cayley
graphs over $Z_2^n$, in which six families are new as we know. By the way, we
formulate the spectra of orbit Cayley graphs as well.
