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The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied over the binary field ℤ2 by Martín del Rey et al. [ Appl. Math. Comput. 217, 8360 (2011)]. Recently, the reversibility problem of 1D Cellular automata with periodic boundary has been extended to ternary fields and further to finite primitive fields ℤp by Cinkir et al. [ J. Stat. Phys. 143, 807 (2011)]. In this work, we restudy some of the work done in Cinkir et al. [ J. Stat. Phys. 143, 807 (2011)] by using a different approach which is based on the theory of error correcting codes. While we reestablish some of the theorems already presented in Cinkir et al. [ J. Stat. Phys. 143, 807 (2011)], we further extend the results to more general cases. Also, a conjecture that is left open in Cinkir et al. [ J. Stat. Phys. 143, 807 (2011)] is also solved here. We conclude by presenting an application to Error Correcting Codes (ECCs) where reversibility of cellular automata is crucial. [ABSTRACT FROM AUTHOR]

In this paper, we study one dimensional finite linear cellular automata with reflective boundary condition by using matrix algebra built on the field ℤp. We present an algorithm for determining the reversibility of this family of cellular automata. We also answer the reversibility question for some special subfamilies. Finally, we present some examples of this family of cellular automata under the reflective boundary condition. [ABSTRACT FROM AUTHOR]