An approach to coding theory and the k-Narayana sequence
Vedat Kabasakalvedatkabasakal@gmail.comDepartment of Mathematics Ankara Haci Bayram Veli UniversityAnkara, Turkey0000-0001-6449-1070View full profile → , *Fatih YılmazCorresponding authorfatih.yilmaz@hbv.edu.trDepartment of Mathematics Ankara Haci Bayram Veli UniversityAnkara, 06900, Turkey0000-0001-7873-1979View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Apr 2024
- Published Online:
- 14 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2197
- Pages:
- 1201–1217
Abstract
Keywords
Subject Classifications
References
[1] Narayana Pandita and Pt. Durgashankar Jyautishacharya, The Ganita Kaumudi, Princess of Wales Sarasvati Bhavana Texts (1942).
[2] Jhon Bravo, Pranabesh Das, and Sergio Sánchez, “Repdigits in Narayana’s Cows Sequence and their consequences,” Journal of Integer Sequences, vol. 23, article 1 (2020).
[3] Yüksel Soykan, “Generalized Fibonacci Numbers: Sum formulas,” Journal of Advances in Mathematics and Computer Science, vol. 35, no. 1, pp. 89–104 (Feb. 2020).
[4] José Ramírez and Victor Sirvent, “A note on the k-Narayana sequence,” Annales Mathematicae et Informaticae, vol. 45, pp. 91–105 (2015).
[5] Engin Özkan, Bahar Kuloğlu, and James Peters, “k-Narayana sequence self-similarity,” HAL Archives Ouvertes, preprint no. 3242990 (2021). [Online]. Available: https://hal.archives-ouvertes.fr/hal-03242990
[6] Xin Lin, “On the recurrence properties of Narayana’s cows sequence,” Symmetry, vol. 13, article 149 (Jan. 2021).
[7] Ramaswamy Sivaraman, “Knowing Narayana cows sequence,” Advances in Mathematics: Scientific Journal, vol. 9, no. 12, pp. 10219–10224 (2020).
[8] Mustafa Aşci and Süleyman Aydınyüz, “k-order Gaussian Fibonacci polynomials and applications to the coding/decoding theory,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, no. 5, pp. 1399–1416 (2022).
[9] Süleyman Aydınyüz and Mustafa Aşci, “Error detection and correction for coding theory on k-order Gaussian Fibonacci matrices,” Mathematical Biosciences and Engineering, vol. 19, no. 5, pp. 4872–4890 (2022).
[10] Jean-Paul Allouche and Tom Johnson, “Narayana’s cows and delayed morphisms,” presented at the Journées d’Informatique Musicale, Île de Tatihou, France (May 1996).
[11] Krishnamurthy Kirthi, “Narayana sequences for cryptographic applications,” arXiv preprint, arXiv:1509.05745 (2015). [Online]. Available: https://arxiv.org/abs/1509.05745
[12] Kisan Bhoi and Prasanta Kumar Ray, “Fermat numbers in Narayana’s cows sequence,” Integers: Electronic Journal of Combinatorial Number Theory, vol. 22 (2022).
[13] Elahe Mehraban and Mansour Baragori, “Coding theory on the generalized balancing sequence,” Notes on Number Theory and Discrete Mathematics, vol. 29, no. 3, pp. 503–524 (Jul. 2023).
[14] Kirthi K. V. and Subhash Kak, “The Narayana Universal Code,” arXiv preprint, arXiv:1601.07110 (2016). [Online]. Available: https://arxiv.org/abs/1601.07110
[15] Roji Bala and V. Mishra, “Narayana matrix sequence,” Proceedings of the Jangjeon Mathematical Society, vol. 25, pp. 427–434 (Nov. 2022).
[16] Sakine Hulk, Özgür Erdağ, and Ömür Deveci, “Complex-type Narayana sequence and its application,” Maejo International Journal of Science and Technology, vol. 17, no. 2 (2023).
[17] Neil J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, vol. 1, p. 130 (Jan. 2007).
