Öz
In this study, we worked on the third-order bivariate variant of the Fibonacci universal code and the second-order bivariate variant of the Narayana universal code, depending on two negative integer variables u and v. We then showed in tables these codes for 1≤k≤100, u=-1,-2,…,-20, and v=-2,-3,…,-21 (u and v are consecutive, v$<$u). Moreover, we obtained some significant results from these tables. Furthermore, we compared the use of these codes in cryptography. Finally, we obtained the third-order bivariate variant of Fibonacci codes is more valuable than the second-order bivariate variant of Narayana codes.
Anahtar Kelimeler
Fibonacci sequence Narayana sequence cryptography variant Fibonacci code variant Narayana Code
Kaynakça
- T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001.
- M. Feinberg, Fibonacci-Tribonacci, The Fibonacci Quarterly 1 (1963) 71–74.
- J. H. Thomas, Variations on the Fibonacci Universal Code. arXiv:0701085 (2007).
- S. Kak, The Golden Mean and the Physics of Aesthetics, in: B. Yadav, M. Mohan (Eds.), Ancient Indian Leaps into Mathematics, Birkhäuser, Boston, 2011, pp. 111–119.
- K. Kirthi, S. Kak, The Narayana Universal Code, arXiv: 1601.07110 (2016).
- T. Buschmann, L.V. Bystrykh, Levenshtein Error-Correcting Barcodes for Multiplexed DNA Sequencing, BMC Bioinformatics 14 (1) (2013) 272.
- E. Zeckendorf, Representation Des Nombres Naturels Par Une Somme Des Nombres De Fibonacci Ou De Nombres De Lucas, Bulletin De La Society Royale des Sciences de Liege 41 (1972) 179–182.
- S. T. Klein, M. K. Ben-Nissan, On the Usefulness of Fibonacci Compression Codes, The Computer Journal 53 (6) (2010) 701–716.
- M. Basu, B. Prasad, Long Range Variant of Fibonacci Universal Code, Journal of Number Theory 130 (2010) 1925–1931.
- A. Nallı, Ç. Özyılmaz, The Third order Variations on the Fibonacci Universal Code, Journal of Number Theory 149 (2015) 15–32.
- D.E. Daykin, Representation of Natural Numbers as Sums of Generalized Fibonacci Numbers, Journal of London Mathematical Society 35 (1960) 143–160.
- M. Basu, M. Das, Uses of Second Order Variant Fibonacci Universal Code in Cryptography, Control and Cybernetics 45 (2) (2016) 239–257.
- M. Das, S. Sinha, A Variant of the Narayana Coding Scheme, Control and Cybernetics 48 (3) (2019) 473–484.
- C. Çimen, S. Akleylek, E. Akyıldız, Şifrelerin Matematiği Kriptografi, ODTÜ Press Ankara, 2007.
- D. R. Stinson, Cryptography Theory and Practice, Chapman & Hall, Ohio, CRC Press, 2002.
Öz
Kaynakça
- T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001.
- M. Feinberg, Fibonacci-Tribonacci, The Fibonacci Quarterly 1 (1963) 71–74.
- J. H. Thomas, Variations on the Fibonacci Universal Code. arXiv:0701085 (2007).
- S. Kak, The Golden Mean and the Physics of Aesthetics, in: B. Yadav, M. Mohan (Eds.), Ancient Indian Leaps into Mathematics, Birkhäuser, Boston, 2011, pp. 111–119.
- K. Kirthi, S. Kak, The Narayana Universal Code, arXiv: 1601.07110 (2016).
- T. Buschmann, L.V. Bystrykh, Levenshtein Error-Correcting Barcodes for Multiplexed DNA Sequencing, BMC Bioinformatics 14 (1) (2013) 272.
- E. Zeckendorf, Representation Des Nombres Naturels Par Une Somme Des Nombres De Fibonacci Ou De Nombres De Lucas, Bulletin De La Society Royale des Sciences de Liege 41 (1972) 179–182.
- S. T. Klein, M. K. Ben-Nissan, On the Usefulness of Fibonacci Compression Codes, The Computer Journal 53 (6) (2010) 701–716.
- M. Basu, B. Prasad, Long Range Variant of Fibonacci Universal Code, Journal of Number Theory 130 (2010) 1925–1931.
- A. Nallı, Ç. Özyılmaz, The Third order Variations on the Fibonacci Universal Code, Journal of Number Theory 149 (2015) 15–32.
- D.E. Daykin, Representation of Natural Numbers as Sums of Generalized Fibonacci Numbers, Journal of London Mathematical Society 35 (1960) 143–160.
- M. Basu, M. Das, Uses of Second Order Variant Fibonacci Universal Code in Cryptography, Control and Cybernetics 45 (2) (2016) 239–257.
- M. Das, S. Sinha, A Variant of the Narayana Coding Scheme, Control and Cybernetics 48 (3) (2019) 473–484.
- C. Çimen, S. Akleylek, E. Akyıldız, Şifrelerin Matematiği Kriptografi, ODTÜ Press Ankara, 2007.
- D. R. Stinson, Cryptography Theory and Practice, Chapman & Hall, Ohio, CRC Press, 2002.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2022 |
| Gönderilme Tarihi | 10 Kasım 2022 |
| Yayımlandığı Sayı | Yıl 2022 Sayı: 41 |
Kaynak Göster
- Makale Dosyaları
|