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

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...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 8; no. 11; p. 2058
Main Authors: Matoušová, Ivana, Trojovský, Pavel
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.11.2020
Subjects:
characteristic equation
Coding
coding theory
Combinatorial analysis
Decoding
Fibonacci numbers
generalizd fibonacci numbers
Mathematics
Numbers
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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 F2(q,n) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence (Tq(n))n=−∞∞, which is an extension of Włoch’s sequence (F2(q,n))n=0∞.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math8112058