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

In this paper, we introduce a new Fibonacci Gp,mGp,m matrix for the m-extension of the Fibonacci p-numbers where p   (⩾0⩾0) is integer and m   (>0). Thereby, we discuss various properties of Gp,mGp,m matrix and the coding theory followed from the Gp,mGp,m matrix. In this paper, we establish the relations among the code elements for all values of p   (nonnegative integer) and m(>0). We also show that the relation, among the code matrix elements for all values of p   and m=1m=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.