Analysis of cellular automata used as pseudorandom pattern generators

The consequences of the similarity transformation between the transition matrix of a linear cellular automaton (CA) and that of a linear feedback shift register (LFSR) are explored. It is shown that the bit sequence from a stage of a CA is identical to that from the LFSR found by the similarity transformation. The concept of discrete algorithms of a binary polynomial is introduced and used with an operational calculus to calculate the phase shift between the bit sequences emitted by different stages of a linear CA. The simulation of hybrid 90/150 CA done during the course of this work leads to some conjectures about the realizability of cellular automata exhibiting maximum length sequences with null and cyclic boundary conditions