Coding theory on generalized Fibonacci n-step polynomials. Issue 1 (2nd January 2017) - Basu, Manjusri; Das, Monojit
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.