In this paper, we introduce h(x) Fibonacci p-numbers polynomials and a new Fibonacci Qp,h(x) matrix for h(x) Fibonacci p-numbers polynomials where p(> 0) is integer and h(x)(> 0) is a polynomial with real coefficients. Thereby, we discuss various properties of Qp,h(x) matrix and the coding theory followed from the Qp,h(x) matrix. We establish the relations among the code matrix elements for p(> 0) is integer and h(x)(> 0). We also show that the relations, among the code matrix elements for h(x) = m (> 0), coincide with the relations among the code matrix elements for coding theory on the m-extension of the Fibonacci p-numbers. The relations among the code matrix elements for h(x) = 1, coincide with the generalized relations among the code matrix elements for Fibonacci coding theory. In general, correct ability of this method, which is independent of h(x), increases as p increases but h(x) being a polynomial, improves the cryptography protection.
['Manjusri Basu', 'Bandhu Prasad']
CODING THEORY ON h(x) FIBONACCI p-NUMBERS POLYNOMIALS