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Reversibility of Symmetric Linear Cellular Automata with Radius r = 3

Author

Listed:
  • A. Martín del Rey

    (Department of Applied Mathematics, IUFFyM, University of Salamanca, 37008-Salamanca, Spain
    Authors contributed equally to this work.)

  • R. Casado Vara

    (BISITE Research Group, University of Salamanca, 37008-Salamanca, Spain
    Authors contributed equally to this work.)

  • D. Hernández Serrano

    (Department of Mathematics, IUFFyM, University of Salamanca, 37008-Salamanca, Spain
    Authors contributed equally to this work.)

Abstract

The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius r = 3 and null boundary conditions. The main result obtained is the explicit computation of the local transition functions of the inverse cellular automata. This allows introduction of possible and interesting applications in digital image encryption.

Suggested Citation

  • A. Martín del Rey & R. Casado Vara & D. Hernández Serrano, 2019. "Reversibility of Symmetric Linear Cellular Automata with Radius r = 3," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:816-:d:263749
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    References listed on IDEAS

    as
    1. Hernández Serrano, D. & Martín del Rey, A., 2019. "A closed formula for the inverse of a reversible cellular automaton with (2R+1)-cyclic rule," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 23-34.
    2. A. Martín Del Rey & G. Rodríguez Sánchez, 2006. "On The Reversibility Of 150 Wolfram Cellular Automata," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 975-983.
    3. A. Martín Del Rey & G. Rodríguez Sánchez, 2009. "Reversibility Of A Symmetric Linear Cellular Automata," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1081-1086.
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    1. Hernández Serrano, D. & Martín del Rey, A., 2019. "A closed formula for the inverse of a reversible cellular automaton with (2R+1)-cyclic rule," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 23-34.

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