In this paper we introduce and study k-order Gaussian Fibonacci Coding
Theory. We give illustrative examples about coding theory. This coding
theory is a method bound to the Q_k, R_k and E_n^(k) matrices.
This coding/decoding method is different from classical algebraic
coding. k-order Gaussian Fibonacci Coding method depends on matrix
multiplication and can be performed quickly and easily by today’s
computers. This method will not only ensures information security in
data transfer but also has high correct ability. Consequently, this
method aims to increase the reliability of information transfer by
moving the coding theory to the complex space.