Fibonacci coding We begin to develop new coding theory based on the -matrices since the simplest Fibonacci
For example our message is the sequence of the decimal numerals:
Then we can represent our message (2) in the matrix form:
Suppose now that we have selected for coding the Fibonacci
At the preceding pages of our Museum we have introduced the notion of the matrix "inverse" to (4). Because the number 5 is odd than the matrix "inverse" to (4) has the following form: Then, the Fibonacci coding of the message
where
For our "unenlightened" reader we remember that the "matrix multiplication" is mathematical operation distinguished from the traditional "multiplication". We can see from the example (5) that the product of two square matrices Let's apply our calculations to our example (3). Then the procedure of the Fibonacci coding brings us into the following matrix After that the code message is sent to the communication channel. The decoding of the code message
Let's calculate the entries of the matrix, which can be obtained after the decoding, taking into consideration (6): Thus, we have: Thus, we have showed a possibility to code and decode the initial numerical information by using the Fibonacci |