Cellular Automata(CA) has been used as modeling and computing paradigm for a long time. And CA has been used to model many physical systems. While studying the models of such systems, it is seen that as the complexity of the physical system increase, the CA based model becomes very complex and difficult to track analytically. Also such models fail to recognize the presence of inherent hierarchical nature of a physical system. In this paper we give the characterization of linear group GF(2~P) CA. Especially we analyze the relationship between characteristic polynomial and transition rule of linear group GF(2~P) CA.
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