We introduce the notion of a symmetric basis of a vector space equipped with
a quadratic form, and provide a sufficient and necessary condition for the
existence to such a basis. Symmetric bases are then used to study Cayley graphs
of certain extraspecial 2-groups of order 2^{2r+1} (r\geq 1), which are further
shown to be normal Cayley graphs and 2-arc-transitive covers of 2r-dimensional
hypercubes

Giudici, Michael