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

A Fibonacci coding method using Fibonacci polynomials is introduced. For integers m≥2m≥2, x≥1x≥1 and n≥1n≥1, an m×mm×m matrix Qmn(x), the nnth power of Qm(x)Qm(x), is considered as the encoding matrix, where QmQm is an m×mm×m matrix whose elements are Fibonacci polynomials. The decoding matrix Qm−n(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 mm large enough. Illustrative examples are provided.