  We give a generalization of Morita's works on ground states of Ising chains,
for chains with a periodic structure with different spins, and distant neighbor
interactions. The main assumption is translational invariance. The length of
the irreducible blocks is a multiple of the period of the chain. In the case of
parity invariance, it restricts the length in general only in the diatomic
case. There are degenerated states and under certain circumstances there could
be nonregular ground states. We illustrate the results and give the ground
state diagrams in several cases.
