Coding theory on the m-extension of the Fibonacci p-numbers

In this paper, we introduce a new Fibonacci Gp;m matrix for the m-extension of the Fibonacci p-numbers where p (P 0) is integer and m (>0). Thereby, we discuss various properties of Gp;m matrix and the coding theory followed from the Gp;m matrix. In this paper, we establish the relations among the code elements for all values of p (nonnegative integer) and m ð> 0Þ. We also show that the relation, among the code matrix elements for all values of p and m ¼ 1, coincides with the relation among the code matrix elements for all values of p [Basu M, Prasad B. The generalized relations among the code elements for Fibonacci coding theory. Chaos, Solitons and Fractals (2008). doi: 10.1016/j.chaos.2008.09.030]. In general, correct ability of the method increases as p increases but it is independent of m.