REVERSIBLE CELLULAR AUTOMATA WITH PENTA-CYCLIC RULE AND ECCs

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Siap I., Akın H., Köroğlu M. E.

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, cilt.23, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1142/s0129183112500660
  • Dergi Adı: INTERNATIONAL JOURNAL OF MODERN PHYSICS C
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Cellular automata, periodic boundary condition, reversibility, matrix representations, ECCs, BLOCK CIPHER, BEHAVIOR
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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 Z(2) by Martin 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 Z(p) 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.