# 2-D Reversible Cellular Automata with Nearest and Prolonged Next Nearest Neighborhoods under Periodic Boundary

Author Name | University of Author | Faculty of Author |
---|---|---|

### Volume:

- 6

### Publication Year:

- 2013

### Number:

- 3

### Publication Language:

- English

### Key Words:

### REFERENCES

[1] H. Akın. On the directional entropy of Z2 -actions generated by additive cellular automata,

Applied Mathematics and Computation. 170 (1), 339-346. 2005.

[2] H. Akın. On the topological directional entropy, Journal of Computational and Applied

Mathematics. 225 (2), 459-466. 2009.

[3] H. Akın and I. Siap. On cellular automata over Galois rings, Information Processing

Letters. 103 (1), 24-27. 2007.

[4] G. Alvarez, L. H. Encinas, and A. Martin del Rey. A multisecret sharing scheme for color

images based on cellular automata, Information Sciences. 178, 4382-4395. 2008.

[5] S.R. Blackburn, S. Murphy, and K.G. Peterson. Comments on theory and applications of

cellular automata in cryptography, IEEE Transactions on Computers. 46, 637-638. 1997.

[6] P. Chattopdhyay, P. P. Choudhury, and K. Dihidar. Characterisation of a particular hybrid

transformation of two-dimensional cellular automata, Computers Mathematics with Applications.

38, 207-216. 1999.

[7] S.J. Cho, U.S. Choi, and S.H. Heo. Design of double error correcting codes based on

cellular automata, Journal of Applied Mathematics and Computing. 21, 545-553. 2006.

REFERENCES 334

[8] D.R. Chowdhury, S. Basu, I.S. Gupta, and P.P. Chaudhuri. Design of CAECC-Cellular

Automata Based Error Correcting Code, IEEE Transactions on Computers. 43, 759-764.

1994.

[9] A. K. Das. Additive cellular automata: Theory and application as a built-in self-test

structure, PH.D. Thesis, I.I.T. Kharagpur, India. 1990.

[10] K. Dihidar and P. P. Choudhury. Matrix algebraic formulae concerning some exceptional

rules of two dimensional cellular automata, Information Sciences 165, 91-101. 2004.

[11] S. Inokuchi and T. Sato. On limit cycles and transient lengths of cellular automata with

threshold rules, Bulletin of Informatics and Cybernetics. 32 (1), 2360. 2000.

[12] A. R. Khan, P. P. Choudhury, K. Dihidar, S. Mitra, and P. Sarkar. VLSI architecture of a

cellular automata, Computers Mathematics with Applications. 33, 79-94. 1997.

[13] A. R. Khan, P. P. Choudhury, K. Dihidar, and R. Verma. Text compression using two dimensional

cellular automata, Computers Mathematics with Applications. 37, 115-127.

1999.

[14] S. Lipschutz. Theory and problems of linear algebra, Mc Graw Hill Inc. 1990.

[15] F.J. MacWilliams and N.J.A Sloane. The Theory Of Error Correcting Codes, North-

Holland Pub. Co., 1977.

[16] M. Mihaljevic, Y. Zheng, and H. Imai. A family of fast dedicated one-way hash functions

based on linear cellular automata over GF(q), IEICE Transactions on Fundamentals E82-

A, 40-47. 1999.

[17] K. Nishinar and D. Takahashi. Multi-value cellular automaton models and metastable

states in a congested phase, Journal of Physics A: Mathematical and General. 33, 7709-

7720. 2000.

[18] I. Siap, H. Akın, and F. Sah. Characterization of two dimensional cellular automata over

ternary fields, Journal of the Franklin Institute, 348, 1258-1275. 2011.

[19] I. Siap, H. Akın, and F. Sah. Garden of Eden configurations for 2-D cellular automaton

with rule 2460N, Information Science. 180 (18), 3562-3571. 20107

[20] I. Siap, H. Akın, and S. Uguz. Structure and reversibility of 2-dimensional hexagonal cellular

automata, Computers Mathematics with Applications, 62(11), 4161-4169. 2011.

[21] J. Von Neumann. The theory of self-reproducing automata, (Edited by A.W.Burks), Univ.

of Illinois Press, Urbana. 1966.

[22] S. Wolfram. Statistical mechanics of cellular automata, Reviews of Modern Physics.

55(3), 601-644. 1983.