Çağla ÇELEMOĞLU

Bivariate Variations of Fibonacci and Narayana Sequences and Universal Codes

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

Keywords:

Fibonacci sequence, Narayana sequence, cryptography, variant Fibonacci code variant Narayana Code,

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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, Foarm Magazine 5, 73–81, arxiv:0411195 (2006).
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.