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On Coding by (2, q )-Distance Fibonacci Numbers

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  • Ivana Matoušová

    (Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic)

  • Pavel Trojovský

    (Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic)

Abstract

In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p -numbers, which he called the Fibonacci coding/decoding method. Stakhov’s papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence of Fibonacci p -numbers. In 2013, I. Włoch et al. studied ( 2 , q ) -distance Fibonacci numbers F 2 ( q , n ) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence ( T q ( n ) ) n = − ∞ ∞ , which is an extension of Włoch’s sequence ( F 2 ( q , n ) ) n = 0 ∞ .

Suggested Citation

  • Ivana Matoušová & Pavel Trojovský, 2020. "On Coding by (2, q )-Distance Fibonacci Numbers," Mathematics, MDPI, vol. 8(11), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2058-:d:446930
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    References listed on IDEAS

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    1. Spiros D. Dafnis & Andreas N. Philippou & Ioannis E. Livieris, 2020. "An Alternating Sum of Fibonacci and Lucas Numbers of Order k," Mathematics, MDPI, vol. 8(9), pages 1-4, September.
    2. Alberto Fiorenza & Giovanni Vincenzi, 2013. "From Fibonacci Sequence to the Golden Ratio," Journal of Mathematics, Hindawi, vol. 2013, pages 1-3, March.
    3. Stakhov, A.P., 2006. "Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 56-66.
    4. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    5. Fiorenza, Alberto & Vincenzi, Giovanni, 2011. "Limit of ratio of consecutive terms for general order-k linear homogeneous recurrences with constant coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 145-152.
    6. Basu, Manjusri & Prasad, Bandhu, 2009. "Coding theory on the m-extension of the Fibonacci p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2522-2530.
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