Research Article

A New Application to Coding Theory via Fibonacci and Lucas Numbers

Volume: 7 Number: 1 April 30, 2019
Sümeyra Uçar , Nihal Taş , Nihal Yılmaz Özgür
EN

A New Application to Coding Theory via Fibonacci and Lucas Numbers

Abstract

Coding/decoding algorithms are of great importance to help in improving information security since
information security is a more significant problem in recent years. In this paper we introduce two new
coding/decoding algorithms using Fibonacci Q-matrices and R-matrices. Our models are based on the
blocked message matrices and the encryption of each message matrix with different keys. These new
algorithms will not only increase the security of information but also has high correct ability.

Keywords

coding/decoding algorithm,Fibonacci Q-matrix,R-matrix; minesweeper

References

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  3. [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. [4] Hoggat, V. E., Fibonacci and Lucas Numbers. Houghton-Mifflin. Palo Alto, 1969.
  5. [5] Koshy, T., Fibonacci and Lucas numbers with applications. New York, NY: JohnWiley and Sons, 2001.
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  8. [8] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
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APA
Uçar, S., Taş, N., & Özgür, N. Y. (2019). A New Application to Coding Theory via Fibonacci and Lucas Numbers. Mathematical Sciences and Applications E-Notes, 7(1), 62-70. https://doi.org/10.36753/mathenot.559251
AMA
1.Uçar S, Taş N, Özgür NY. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. 2019;7(1):62-70. doi:10.36753/mathenot.559251
Chicago
Uçar, Sümeyra, Nihal Taş, and Nihal Yılmaz Özgür. 2019. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes 7 (1): 62-70. https://doi.org/10.36753/mathenot.559251.
EndNote
Uçar S, Taş N, Özgür NY (April 1, 2019) A New Application to Coding Theory via Fibonacci and Lucas Numbers. Mathematical Sciences and Applications E-Notes 7 1 62–70.
IEEE
[1]S. Uçar, N. Taş, and N. Y. Özgür, “A New Application to Coding Theory via Fibonacci and Lucas Numbers”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 62–70, Apr. 2019, doi: 10.36753/mathenot.559251.
ISNAD
Uçar, Sümeyra - Taş, Nihal - Özgür, Nihal Yılmaz. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes 7/1 (April 1, 2019): 62-70. https://doi.org/10.36753/mathenot.559251.
JAMA
1.Uçar S, Taş N, Özgür NY. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. 2019;7:62–70.
MLA
Uçar, Sümeyra, et al. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, Apr. 2019, pp. 62-70, doi:10.36753/mathenot.559251.
Vancouver
1.Sümeyra Uçar, Nihal Taş, Nihal Yılmaz Özgür. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. 2019 Apr. 1;7(1):62-70. doi:10.36753/mathenot.559251

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