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In this paper, we introduce a new complex Fibonacci matrix H p , n whose elements are complex Fibonacci numbers and we developed a new coding and decoding method followed from this complex Fibonacci matrix H p , n . We establish the relations among the code matrix elements, error detection and correction for this coding theory. [ABSTRACT FROM AUTHOR]

In [K. Kuhapatanakul, The Lucas -matrix, Internat. J. Math. Ed. Sci. Tech. (2015), http://dx.doi.org/10.1080/0020739X.2015.1026612], Kuhapatanakul introduced Lucas matrix, whose elements are Lucas numbers. In this paper, we developed a new coding and decoding method followed from Lucas matrix, . We established the relations among the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is % for and for , the correction ability is %. In general, correction ability of this method increases as increases. [ABSTRACT FROM AUTHOR]

In this paper, we introduced h(x) extension of m sequences of Fibonacci numbers polynomials of order m and a new Sn matrix of order m where h(x)(> 0) is a polynomial with real coefficients. Thereby, we discuss various properties of Sn matrix and the Fibonacci coding theory followed from this matrix. We established the relations among the code matrix elements, error deduction and correction for this coding theory. In general, correct ability potential of this method increases and it is independent of h(x). But h(x) being a polynomial, improves the cryptography protection. [ABSTRACT FROM AUTHOR]

In this paper, a new class of square matrix of order pm is introduced, where (p = 3, 4, 5, ...), (m = 1, 2, 3, ...) and for integers n, x ≥ 1. Fibonacci polynomial coding and decoding methods are followed from matrix and high code rates are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we develop hybrid matrix cryptography followed by Fibonacci Qp,h(x) matrix, where h(x) is a polynomial with real coefficients and p = 1, 2, 3,.... They are the generalization of classical Fibonacci Q matrix for a continuous domain. They are used for designing super reliable cryptosystems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Fibonacci coding is based on Fibonacci numbers and was defined by Apostolico and Fraenkel (1987) . Fibonacci numbers are generated by the recurrence relation with initial terms , . Variations on the Fibonacci coding are used in source coding as well as in cryptography. In this paper, we have extended the table given by Thomas . We have found that there is no Gopala–Hemachandra code for a particular positive integer n and for a particular value of . We conclude that for , Gopala–Hemachandra code exists for . Also, for , there is at most m consecutive not available (N/A) Gopala–Hemachandra code in column where . And, for , as m increases the availability of Gopala–Hemachandra code decreases in column where . [Copyright &y& Elsevier]