Coding theory on generalized Fibonacci n-step polynomials. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Basu, Manjusri; Das, Monojit
• Is Part Of: Journal of information & optimization sciences. Volume 38:Issue 1(2017)
• Page Start: 83
• Page End: 131
• Publication Date: 2017-01-02
• Subjects: Fibonacci numbers -- Fibonacci n-step numbers -- Fibonacci polynomials -- Fibonacci n-step polynomials -- generalized Fibonacci n-step polynomials -- generalized Fibonacci n-step polynomial coding -- error correction; Electronic data processing -- Periodicals; Information science -- Periodicals; Mathematical optimization -- Periodicals; 519.6
• DOI: 10.1080/02522667.2016.1160618
• Languages: English
• ISSNs: 0252-2667

Abstract

Abstract: In this paper, we introduce generalized Fibonacci n -step polynomials. Based on generalized Fibonacci n -step polynomials, we define a new class of square matrix Mh, n ( x ) of order n . Thereby, we state a new coding theory called generalized Fibonacci n -step polynomial coding theory. Also we obtain the relations among the code matrix elements. Next, we discuss on the correct ability of this method. It is shown that, for n = 2, the correct ability of this method is 93.33% whereas for n = 3, the correct ability of this method is 99.80%. The interesting part of this coding/decoding method is that the correct ability does not depend on the polynomial coefficients excepting the value of the n th coefficient hn ( x ) = 1 and increases as n increases.