Analysis of one-dimensional linear hybrid cellular automata over GF(q)

The paper studies theoretical aspects of one dimensional linear hybrid cellular automata over a finite (Galois) field. General results concerning the characteristic polynomials of such automata are presented. A probabilistic synthesis algorithm for determining such a linear hybrid cellular automaton with a specific characteristic polynomial is given, along with empirical results and a theoretical analysis. Cyclic boundary cellular automata are defined and related to the more common null boundary cellular automate. An explicit similarity transform between a cellular automaton and its corresponding linear feedback shift register is derived.