  For a K3 surface of finite height over a field of odd characteristic, there
exists a smooth lifting to the ring of Witt vectors such that the reduction map
from the Picard group of the generic fiber to the Picard group of the special
fiber is isomorphic. In this paper, using this result, we give a criterion for
a K3 surface of finite height over a field of odd characteristic to be an
Enriques K3 surface or to be a K3 surface in terms of the Neron-Severi lattice.
Then we show every Kummer surface has an Enriques involution. We also give a
classification of K3 surfaces of Picard rank of 20 over odd characteristic.
