Review Article

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

Volume: 8 Number: 1 February 14, 2025
Şükran Uygun *, Ersen Akıncı
EN

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

Abstract

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.

Keywords

Encoding-Decoding algorithms, Jacobsthal sequence, Jacobsthal- Lucas sequence

References

  1. [1] Horadam, A. F., Jacobsthal representation numbers, The Fibonacci Quar- terly.,37(2), (1996), 40-52.
  2. [2] Stakhov, A., Massingue, V. and Sluchenkov, A., Introduction into Fi- bonacci coding and cryptography. Osnova, Kharkov, 1999.
  3. [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. [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. [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. [6] Tahghighi, M., Jafaar, A. R. Mahmod, Generalization of Golden Cryptog- raphy based on k-Fibonacci Numbers in (ICINC) at 2010.
  7. [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. [8] Esmaeili, M., Esmaeili, M., Fibonacci-polynomial based coding method with error detection and correction, Comput. Math. Appl. 60(10), (2010),2738-2752.
  9. [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. [10] Prasad, B., Coding theory on Lucas p-numbers. Discrete Math. Algorithms Appl. 8 (2016), no.4, 17 pages.
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. https://izlik.org/JA56WH95PZ
AMA
1.Uygun Ş, Akıncı E. A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers. JAMAME. 2025;8(1):1-11. https://izlik.org/JA56WH95PZ
Chicago
Uygun, Şükran, and Ersen Akıncı. 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. https://izlik.org/JA56WH95PZ.
EndNote
Uygun Ş, Akıncı E (February 1, 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.
IEEE
[1]Ş. Uygun and E. Akıncı, “A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers”, JAMAME, vol. 8, no. 1, pp. 1–11, Feb. 2025, [Online]. Available: https://izlik.org/JA56WH95PZ
ISNAD
Uygun, Şükran - Akıncı, Ersen. “A New Application to Coding Theory via Generalized Jacobsthal and Jacobsthal-Lucas Numbers”. Journal of Advanced Mathematics and Mathematics Education 8/1 (February 1, 2025): 1-11. https://izlik.org/JA56WH95PZ.
JAMA
1.Uygun Ş, Akıncı E. A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers. JAMAME. 2025;8:1–11.
MLA
Uygun, Şükran, and Ersen Akıncı. “A New Application to Coding Theory via Generalized Jacobsthal and Jacobsthal-Lucas Numbers”. Journal of Advanced Mathematics and Mathematics Education, vol. 8, no. 1, Feb. 2025, pp. 1-11, https://izlik.org/JA56WH95PZ.
Vancouver
1.Şükran Uygun, Ersen Akıncı. A New Application to Coding Theory via generalized Jacobsthal and Jacobsthal-Lucas Numbers. JAMAME [Internet]. 2025 Feb. 1;8(1):1-11. Available from: https://izlik.org/JA56WH95PZ