  Higher-order topological phases (HOTPs) are characterized by
symmetry-protected bound states at the corners or hinges of the system. In this
work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven
systems, which are demonstrated in a two-dimensional extension of the quantum
double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry
and characterized by a pair of topological invariants, which could take
arbitrarily large integer values with the increase of kicking strengths. These
topological numbers can also be measured from the chiral dynamics of wave
packets. Under open boundary conditions, multiple quartets Floquet corner modes
with zero and $\pi$ quasienergies emerge in the system and coexist with
delocalized bulk states at the same quasienergies, forming second-order Floquet
topological bound states in continuum. The numbers of these corner modes are
further counted by the bulk topological invariants according to the relation of
bulk-corner correspondence. Our findings thus extend the study HOTPs to
momentum-space lattices, and further uncover the richness of HOTPs and
corner-localized bound states in continuum in Floquet driven systems.
