  Diameter perfect codes form a natural generalization for perfect codes. They
are based on the code-anticode bound which generalizes the sphere-packing
bound. The code-anticode bound was proved by Delsarte for distance-regular
graphs and it holds for some other metrics too. In this paper we prove the
bound for non-binary constant-weight codes with the Hamming metric and
characterize the diameter perfect codes and the maximum size anticodes for
these codes. We distinguish between six families of non-binary diameter
constant-weight codes and four families of maximum size non-binary
constant-weight anticodes. Each one of these families of diameter perfect codes
raises some different questions. We consider some of these questions and leave
lot of ground for further research. Finally, as a consequence, some
t-intersecting families related to the well-known Erd\"{o}s-Ko-Rado theorem,
are constructed.
