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In this paper, we introduce a Qn2(x) matrix, whose elements are balancing polynomials, and develop a new coding and decoding method following from the Qn2(x) matrix. We establish the relations between the code matrix elements, error detection and correction for this coding theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the h(x) Lucas polynomials of order m and the Un matrix, whose elements are Lucas polyno- mials, h(x)(> 0) being a polynomial with real coefficients. We also establish the relations among the code matrix elements. [ABSTRACT FROM AUTHOR]

Fibonacci codes of different orders are of variable length. They are used for encoding of numbers and find applications in information and coding theory. The Fibonacci binary encoding and computation of its values are closely associated with Fibonacci shift operations. Walder et al. (2012) established a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 2, 3. In this paper, we establish a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 4 and we generalize the formula for kth Fibonacci left shift for the Fibonacci numbers of all orders. [ABSTRACT FROM AUTHOR]

In this paper, we introduce multivariable extension of m sequences of the Fibonacci number polynomials of order m and a new Sn matrix of order m. Consequently, we discuss various properties of the Sn matrix. The polynomial, derived therefrom, hj, contains m multiple variables which improves the cryptography protection and security, and complexity increases as m increases. [ABSTRACT FROM AUTHOR]