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

Ivana Matoušová and Pavel Trojovský
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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

Mathematics, 2020, vol. 8, issue 11, 1-24

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. W?och 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 W?och’s sequence ( F 2 ( q , n ) ) n = 0 ∞ .

Keywords: fibonacci numbers; generalizd fibonacci numbers; characteristic equation; coding theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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