THE MOORE-PENROSE INVERSE OF THE RECTANGULAR FIBONACCI MATRIX AND APPLICATIONS TO THE CRYPTOLOGY

Abstract

In this paper, we define the general form of the Moore-Penrose inverse for the matrix whose elements are Fibonacci numbers. We examine the states of the matrix F e Mm ,n(C), where F is a rectangular Fibonacci matrix based on the values of m and n. In the second part of this study, we introduce a novel coding theory using the Moore-Penrose inverse of the rectangular Fibonacci matrix and provide illustrative examples. The rectangular Fibonacci matrix plays a crucial role in the construction of the coding algorithm. This coding method is referred to as the coding theory on rectangular Fibonacci matrix.