  This paper examines the relationship between the automorphism group of a
hyperelliptic curve defined over an algebraically closed field of
characteristic two and the 2-rank of the curve. In particular, we exploit the
wild ramification to use the Deuring-Shafarevich formula in order to analyze
the ramification of hyperelliptic curves that admit extra automorphisms and use
this data to impose restrictions on the genera and 2-ranks of such curves. We
also show how some of the techniques and results carry over to the case where
our base field is of characteristic $p>2$.
