A New Application to Coding Theory via Fibonacci and Lucas Numbers
Coding/decoding algorithms are of great importance to help in improving information security since
___
- [1] Basu, M. and Prasad, B., The generalized relations among the code elements for Fibonacci coding theory. Chaos
Solitons Fractals 41 (2009), no. 5, 2517-2525.
- [2] Bruggles I. D. and Jr Hoggatt, V. E., A Primer for the Fibonacci numbers-Part IV. Fibonacci Q. 1 (1963), no.4,
65-71.
- [3] Gould, H.W., A history of the Fibonacci Q-matrix and a higher-dimensional problem. Fibonacci Quart. 19 (1981),
no. 3, 250-257.
- [4] Hoggat, V. E., Fibonacci and Lucas Numbers. Houghton-Mifflin. Palo Alto, 1969.
- [5] Koshy, T., Fibonacci and Lucas numbers with applications. New York, NY: JohnWiley and Sons, 2001.
- [6] Kuhapatanakul, K., The Lucas p-matrix. Internat. J. Math. Ed. Sci. Techn. (2015).
http://dx.doi.org/10.1080/0020739X.2015.1026612
- [7] Prajapat, S., Jain, A. and Thakur, R. S., A novel approach for information security with automatic variable key
using Fibonacci Q-matrix. IJCCT 3 (2012), no. 3, 54-57.
- [8] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
- [9] Stakhov, A. P., A generalizition of the Fibonacci Q-matrix. Rep. Natl. Acad. Sci. Ukraine 9 (1999), 46-49.
- [10] Stakhov, A., Massingue, V. and Sluchenkov, A., Introduction into Fibonacci coding and cryptography. Osnova,
Kharkov, 1999.
- [11] Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory. Chaos
Solitons Fractals 30 (2006), no. 1, 56-66.
- [12] Tarle, B. S. and Prajapati, G. L., On the information security using Fibonacci series. International Conference
and Workshop on Emerging Trends in Technology (ICWET 2011)-TCET, Mumbai, India.
- [13] Taş, N., Uçar, S., Özgür, N. Y. and Kaymak, Ö. Ö., A new coding/decoding algorithm using Finonacci numbers.
Discrete Math. Algorithms Appl. 10 (2018), no. 02, 1850028.
- [14] Wang, F., Ding, J., Dai, Z. and Peng, Y., An application of mobile phone encryption based on Fibonacci structure
of chaos. 2010 Second WRI World Congress on Software Engineering.