Coding theory on (h(x); g(y))-extension of Fibonacci p-numbers polynomials

摘要

In this paper, we define (h(x); g(y))-extension of the Fibonacci p-numbers. We also define golden (p; h(x); g(y))-proportions where p (p = 0; 1; 2; 3; ) and h(x)(> 0), g(y)(> 0) are polynomials with real coefficients. The relations among the code elements of a new Fibonacci matrix, Gp;h;g, (p = 0; 1; 2; 3; ), h(x) (> 0), g(y) (> 0) coincide with the relations among the code matrix for all values of p and h(x) = m(> 0) and g(y) = t(> 0) [8]. Also, the relations among the code matrix elements for h(x) = 1 and g(y) = 1, coincide with the generalized relations among the code matrix elements for Fibonacci coding theory [6]. By suitable selection for the initial terms in (h(x); g(y))-extension of the Fibonacci p-numbers, a new Fibonacci matrix, Gp;h;g is applicable for Fibonacci coding/decoding. The correct ability of this method, increases as p increases but it is independent of h(x) and g(y). But h(x) and g(y) being polynomials, improves the cryptography protection. And complexity of this method increases as the degree of the polynomials h(x) and g(y) increases. We have also find a relation among golden (p; h(x); g(y))-proportion, golden (p; h(x))-proportion and golden p-proportion.