  In this note we study a class of one-dimensional Ising chain having a highly
degenerated set of ground-state configurations. The model consists of spin
chain having infinite-range pair interactions with a given structure. We show
that the set of ground-state configurations of such a model can be fully
characterized by means of symbolic dynamics. Particularly we found that the set
ground- state configurations defines what in symbolic dynamics is called sofic
shift space. Finally we prove that this system has a non-vanishing residual
entropy (the topological entropy of the shift space), which can be exactly
calculated.
