A Fibonacci-polynomial based coding method with error detection and correction

A Fibonacci coding method using Fibonacci polynomials is introduced. For integers m ≥ 2, x ≥ 1 and n ≥ 1, an m × m matrix Qnm (x), the nth power of Qm(x), is considered as the encoding matrix, where Qm is anm×mmatrix whose elements are Fibonacci polynomials. The decoding matrix Q−n m (x) is also introduced. A simple error-detecting criterion and a simple error-correcting method for this class of codes are given. It is shown that the probability of decoding error is almost zero for m large enough. Illustrative examples are provided.