TWMS J. App. & Eng. Math, cilt.4, ss.215-225, 2013 (ESCI İndekslerine Giren Dergi)
t. In this paper, we introduce a family of one dimensional finite linear cellular automata with periodic boundary condition over primitive finite fields with p elements (Zp) which
leads to a generalization in two directions: the radius and the field that states take values.
This family of cellular automata is called (2r + 1)-cyclic cellular automata since it has a cyclic
structure and its radius is r. Here, we establish a connection between the generator matrices
of cyclic codes and the rule matrix of (2r + 1)-cyclic cellular automata. Thus this enables the
determination of the reversibility problem of this cellular automaton by means of the algebraic
coding theory. Further, we explicitly determine the reverse CA of this family and prove that
the reverse CA of this family again falls into this family.