Fibonacci shift operation on Fibonacci numbers of order m

• Autorzy: Prasad B.
• Języki publikacji: EN

Abstrakty

EN

Fibonacci codes of different orders are of variable length. They are used for encoding of numbers and find applications in information and coding theory. The Fibonacci binary encoding and computation of its values are closely associated with Fibonacci shift operations. Walder et al. (2012) established a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 2,3. In this paper, we establish a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 4 and we generalize the formula for kth Fibonacci left shift for the Fibonacci numbers of all orders.

Słowa kluczowe

EN

Fibonacci numbers; Fibonacci numbers of order m; golden mean; Fibonacci shift operations

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2016
• Tom: Vol. 45, no. 2
• Strony: 259--266
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Prasad B.

• Department of Mathematics Kandi Raj College Kandi - 742137, India

Bibliografia

• [1] Apostolico A. and Fraenkel A. (1987) Robust transmission of unbounded strings using Fibonacci representations. IEEE Trans. on Information Theory 33, 238–245.
• [2] Esmaeeili M., Gulliver T.A., Kakhbod A. (2009) The Golden mean, Fibonacci matrices and partial weakly super-increasing sources. Chaos, Solitons and Fractals 42, 435–440.
• [3] Basu M., Prasad B. (2009) The generalized relations among the code elements for Fibonacci coding theory. Chaos, Solitons and Fractals 41, 2517–2525.
• [4] Basu M., Prasad B. (2010) Long range variations on the Fibonacci universal code. Journal of Number Theory 130, 1925–1931.
• [5] Stakhov A.P. (1977) Introduction into algorithm measurement theory. Soviet Radio, Moscow (In Russian). Stakhov A.P. (2007) The golden matrices and a new kind of cryptography. Chaos, Solitons and Fractals 32, 1138–1146.
• [6] Walder J., Kratky M., Baca R., Platos J., Snasel V. (2012) Fast decoding algorithms for variable-length codes. Information Sciences 183 66–91.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).