The following details the calculation of the high order entropies of k neighboring or non-neighboring sites of the linear (1D) Ising system. The system has no intrinsic dynamics, and stochastic dynamics are not considered. Limits as the number of spins in the complete system is increased and as the number of sites being considered is increased are considered. Information correlation functions of the sites are investigated and found to give quantities which are the mutual information between the first and last sites of those considered in the chain up to a sign. Graphs show that the information correlation function indicate where in the phase space of the system the high order distribution functions provide new information.