  We discuss a topological classification of insulators and superconductors in
the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer
classification and spatial reflection symmetry in any spatial dimensions. By
using the structure of bulk Dirac Hamiltonians of minimal matrix dimensions and
explicit constructions of topological invariants, we provide the complete
classification, which still has the same dimensional periodicities with the
original Altland-Zirnbauer classification. The classification of
reflection-symmetry-protected topological insulators and superconductors
depends crucially on the way reflection symmetry operation is realized. When a
boundary is introduced, which is reflected into itself, these non-trivial
topological insulators and superconductors support gapless modes localized at
the boundary.
