A New Coding Theory on Fibonacci n-Step Polynomials

Abstract

In this paper, we develop a new series of Fibonacci -step polynomials. Based on these series of polynomials, we introduce a new class of square matrix of order . Thereby, we define a new coding theory called Fibonacci \udc8f-step polynomials coding theory. Then we calculate the generalized relations among the code elements for all values of . It is shown that, for = 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 \udc65 and increases as increases.