İnceleme Makalesi
BibTex RIS Kaynak Göster
Yıl 2025, Cilt: 8 Sayı: 1, 1 - 11, 14.02.2025

Öz

Kaynakça

  • [1] Horadam, A. F., Jacobsthal representation numbers, The Fibonacci Quar- terly.,37(2), (1996), 40-52.
  • [2] Stakhov, A., Massingue, V. and Sluchenkov, A., Introduction into Fi- bonacci coding and cryptography. Osnova, Kharkov, 1999.
  • [3] Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory, Chaos Solitons Fractals 30(1), (2006), 56-66.
  • [4] Basu, M., Prasad, B., The generalized relations among the code elements for Fibonacci coding theory. Chaos Solitons Fractals 41(5), (2009), 2517-2525
  • [5] Wang, F., Ding, J., Dai, Z., Peng, Y., An application of mobile phone encryption based on Fibonacci structure of chaos. 2010 Second WRIWorld Congress on Softwa Engineering.
  • [6] Tahghighi, M., Jafaar, A. R. Mahmod, Generalization of Golden Cryptog- raphy based on k-Fibonacci Numbers in (ICINC) at 2010.
  • [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), 3, 54-57.
  • [8] Esmaeili, M., Esmaeili, M., Fibonacci-polynomial based coding method with error detection and correction, Comput. Math. Appl. 60(10), (2010),2738-2752.
  • [9] Gong, Y.,. Jiang Z., Gao, Y., On Jacobsthal and Jacobsthal-Lucas circu- lant type matrices, Abstract and Applied Analysis, Article ID 418293, 11,(2015).
  • [10] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
  • [11] Tas, N., Ucar, S., Ozgur, N. Y., Kaymak,O. O , A new coding/decoding algorithm using Finonacci numbers, Discrete Mathematics, Algorithms and Applications, 2 (2018),1850028.
  • [12] Uçar,S. Ozgur, N. Y., Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory, J. BAUN Inst. Sci. Technol.21(1), (2019), 306-322.

A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers

Yıl 2025, Cilt: 8 Sayı: 1, 1 - 11, 14.02.2025

Öz

Coding/decoding algorithms carry out vital importance to providing information security since information security is very important for all people in recent years. In this study, we consider two new coding/decoding algorithms by means of J-matrices with elements generalized Jacobsthal and Jacobsthal-Lucas numbers. We used blocked message matrices for our models and we have di¤erent keys for the encryption of each message matrix. These new algorithms will give us opportunity for increasing the security of information and high correct ability.

Kaynakça

  • [1] Horadam, A. F., Jacobsthal representation numbers, The Fibonacci Quar- terly.,37(2), (1996), 40-52.
  • [2] Stakhov, A., Massingue, V. and Sluchenkov, A., Introduction into Fi- bonacci coding and cryptography. Osnova, Kharkov, 1999.
  • [3] Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory, Chaos Solitons Fractals 30(1), (2006), 56-66.
  • [4] Basu, M., Prasad, B., The generalized relations among the code elements for Fibonacci coding theory. Chaos Solitons Fractals 41(5), (2009), 2517-2525
  • [5] Wang, F., Ding, J., Dai, Z., Peng, Y., An application of mobile phone encryption based on Fibonacci structure of chaos. 2010 Second WRIWorld Congress on Softwa Engineering.
  • [6] Tahghighi, M., Jafaar, A. R. Mahmod, Generalization of Golden Cryptog- raphy based on k-Fibonacci Numbers in (ICINC) at 2010.
  • [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), 3, 54-57.
  • [8] Esmaeili, M., Esmaeili, M., Fibonacci-polynomial based coding method with error detection and correction, Comput. Math. Appl. 60(10), (2010),2738-2752.
  • [9] Gong, Y.,. Jiang Z., Gao, Y., On Jacobsthal and Jacobsthal-Lucas circu- lant type matrices, Abstract and Applied Analysis, Article ID 418293, 11,(2015).
  • [10] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
  • [11] Tas, N., Ucar, S., Ozgur, N. Y., Kaymak,O. O , A new coding/decoding algorithm using Finonacci numbers, Discrete Mathematics, Algorithms and Applications, 2 (2018),1850028.
  • [12] Uçar,S. Ozgur, N. Y., Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory, J. BAUN Inst. Sci. Technol.21(1), (2019), 306-322.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers
Yazarlar

Şükran Uygun 0000-0002-7878-2175

Ersen Akıncı Bu kişi benim

Yayımlanma Tarihi 14 Şubat 2025
Gönderilme Tarihi 29 Temmuz 2024
Kabul Tarihi 7 Şubat 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 1

Kaynak Göster

APA Uygun, Ş., & Akıncı, E. (2025). A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers. Journal of Advanced Mathematics and Mathematics Education, 8(1), 1-11.