Error detection and correction for coding theory on k-order Gaussian Fibonacci matrices

In this study, the coding theory defined for k-order Gaussian Fibonacci polynomials is rearranged by taking <inline-formula><tex-math id="M1">\begin{document}$ x = 1 $\end{document}</tex-math></inline-formula>. We call this coding theory the k-order Gaussian Fibonac...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Mathematical biosciences and engineering : MBE Ročník 20; číslo 2; s. 1993 - 2010
Hlavní autoři:	Aydinyuz, Suleyman, Asci, Mustafa
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States AIMS Press 01.01.2023
Témata:	error detection and correction fibonacci numbers gaussian fibonacci numbers k-order gaussian fibonacci coding/decoding k-order gaussian fibonacci matrices k-order gaussian fibonacci numbers Gaussian Fibonacci numbers error detection and correction k-order Gaussian Fibonacci coding/decoding k-order Gaussian Fibonacci numbers Fibonacci numbers k-order Gaussian Fibonacci matrices
ISSN:	1551-0018, 1551-0018
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	In this study, the coding theory defined for k-order Gaussian Fibonacci polynomials is rearranged by taking <inline-formula><tex-math id="M1">\begin{document}$ x = 1 $\end{document}</tex-math></inline-formula>. We call this coding theory the k-order Gaussian Fibonacci coding theory. This coding method is based on the <inline-formula><tex-math id="M2">\begin{document}$ {Q_k}, {R_k} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ E_n^{(k)} $\end{document}</tex-math></inline-formula> matrices. In this respect, it differs from the classical encryption method. Unlike classical algebraic coding methods, this method theoretically allows for the correction of matrix elements that can be infinite integers. Error detection criterion is examined for the case of <inline-formula><tex-math id="M4">\begin{document}$ k = 2 $\end{document}</tex-math></inline-formula> and this method is generalized to <inline-formula><tex-math id="M5">\begin{document}$ k $\end{document}</tex-math></inline-formula> and error correction method is given. In the simplest case, for <inline-formula><tex-math id="M6">\begin{document}$ k = 2 $\end{document}</tex-math></inline-formula>, the correct capability of the method is essentially equal to 93.33%, exceeding all well-known correction codes. It appears that for a sufficiently large value of <inline-formula><tex-math id="M7">\begin{document}$ k $\end{document}</tex-math></inline-formula>, the probability of decoding error is almost zero.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1551-0018 1551-0018
DOI:	10.3934/mbe.2023092