A New Application to Coding Theory via Fibonacci and Lucas Numbers

Sümeyra Uçar; Nihal Taş; Nihal Yılmaz Özgür

doi:10.36753/mathenot.559251

Araştırma Makalesi

A New Application to Coding Theory via Fibonacci and Lucas Numbers

Yıl 2019, , 62 - 70, 30.04.2019

Sümeyra Uçar , Nihal Taş Nihal Yılmaz Özgür

https://doi.org/10.36753/mathenot.559251

Cited By: 19

Öz

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.

Anahtar Kelimeler

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

Kaynakça

[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.

Yıl 2019, , 62 - 70, 30.04.2019

Sümeyra Uçar , Nihal Taş Nihal Yılmaz Özgür

https://doi.org/10.36753/mathenot.559251

Cited By: 19

Öz

Kaynakça

[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.

Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Articles
Yazarlar	Sümeyra Uçar Nihal Taş Nihal Yılmaz Özgür
Yayımlanma Tarihi	30 Nisan 2019
Gönderilme Tarihi	18 Ocak 2018
Yayımlandığı Sayı	Yıl 2019

Kaynak Göster

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	Uçar S, Taş N, Özgür NY. A New Application to Coding Theory via Fibonacci and Lucas Numbers. Math. Sci. Appl. E-Notes. Nisan 2019;7(1):62-70. doi:10.36753/mathenot.559251
Chicago	Uçar, Sümeyra, Nihal Taş, ve Nihal Yılmaz Özgür. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes 7, sy. 1 (Nisan 2019): 62-70. https://doi.org/10.36753/mathenot.559251.
EndNote	Uçar S, Taş N, Özgür NY (01 Nisan 2019) A New Application to Coding Theory via Fibonacci and Lucas Numbers. Mathematical Sciences and Applications E-Notes 7 1 62–70.
IEEE	S. Uçar, N. Taş, ve N. Y. Özgür, “A New Application to Coding Theory via Fibonacci and Lucas Numbers”, Math. Sci. Appl. E-Notes, c. 7, sy. 1, ss. 62–70, 2019, doi: 10.36753/mathenot.559251.
ISNAD	Uçar, Sümeyra vd. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes 7/1 (Nisan 2019), 62-70. https://doi.org/10.36753/mathenot.559251.
JAMA	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 vd. “A New Application to Coding Theory via Fibonacci and Lucas Numbers”. Mathematical Sciences and Applications E-Notes, c. 7, sy. 1, 2019, ss. 62-70, doi:10.36753/mathenot.559251.
Vancouver	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.