Coding Theory on the (M, T)-Extension of the Fibonacci P-numbers

In this paper, we define (m, t)-extension of the Fibonacci p-numbers and Golden (p, m, t)-proportions, where p ≥ 0 is integer, m > 0, and t > 0. We establish a relation among golden (p, m, t)-proportion, golden (p, m)-proportion and golden p-proportion. Thereby, we define a new Fibonacci Gp, m, t matrix. Then we show that by proper selection of the initial terms for the (m, t)-extension of the Fibonacci p-numbers, we can apply Fibonacci coding/decoding in Gp, m, t matrix. Also it is obvious that for t = 1, the relations among the code elements for all values of p (non-negative integer) and m (> 0) coincide with the relations among the code matrix elements for all values of p and m (> 0) with the same initial terms (see the paper coding theory on the m-extension of the Fibonacci p-numbers, Chaos, Solitons and Fractals42 (2009) 2522–2530).

[1]  Manjusri Basu,et al.  The generalized relations among the code elements for Fibonacci coding theory , 2009 .

[2]  M. E. Naschie,et al.  A review of E infinity theory and the mass spectrum of high energy particle physics , 2004 .

[3]  Alexey Stakhov,et al.  The “golden” hyperbolic models of Universe , 2007 .

[4]  Manjusri Basu,et al.  Coding theory on the m-extension of the Fibonacci p-numbers , 2009 .

[5]  Alexey Stakhov,et al.  The “golden” matrices and a new kind of cryptography , 2007 .

[6]  M.S. El Naschie,,et al.  A Review of Applications and Results of Ε-infinity Theory , 2007 .

[7]  Ángel Plaza,et al.  On k-Fibonacci sequences and polynomials and their derivatives , 2009 .

[8]  A B Bruce.  THE GOLDEN MEAN. , 1914, Science.

[9]  M. S. El Naschie,et al.  The theory of Cantorian spacetime and high energy particle physics (an informal review) , 2009 .

[10]  Paul Shorey.  Gnomon , 1925, Classical Philology.

[11]  A. Stakhov.  Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory , 2006 .

[12]  Alexey Stakhov,et al.  The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic , 2007 .

[13]  Alexey Stakhov,et al.  On the m-extension of the Fibonacci and Lucas p-numbers , 2009 .

[14]  Ángel Plaza,et al.  The k-Fibonacci sequence and the Pascal 2-triangle , 2007 .

[15]  Alexey Stakhov.  The Golden Section , 2009 .

[16]  M. S. El Naschie,et al.  Topics in the mathematical physics of E-infinity theory , 2006 .

[17]  Ali Kakhbod,et al.  The Golden mean, Fibonacci matrices and partial weakly super-increasing sources , 2009 .

[18]  Emrah Kilic,et al.  The Binet formula, sums and representations of generalized Fibonacci p-numbers , 2008, Eur. J. Comb..

[19]  Alexey Stakhov,et al.  The golden section, secrets of the Egyptian civilization and harmony mathematics , 2006 .