The Golden mean, Fibonacci matrices and partial weakly super-increasing sources

Esmaeili, Morteza; Gulliver, T. Aaron; Kakhbod, Ali

doi:10.1016/j.chaos.2009.01.007

Cited by 10 publications

(4 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later the Fibonacci numbers were found in many natural objects and phenomena. Now a days Fibonacci numbers [2,10,11] are used in sciences, arts and more recently in combinatorial design theory, high energy physics, information and coding theory [5,7]. The Fibonacci numbers F n (n = 0, ±1, ±2, ±3, .…”

Section: Introductionmentioning

confidence: 99%

Coding theory on (h(x); g(y))-extension of Fibonacci p-numbers polynomials

Prasad¹

2014

ujcmj

View full text Add to dashboard Cite

In this paper, we define (h(x), g(y))-extension of the Fibonacci p-numbers. We also define golden (p, h(x), g(y))-proportions where p (p = 0, 1, 2, 3, • • • ) and h(x)(> 0), g(y)(> 0) are polynomials with real coefficients. The relations among the code elements of a new Fibonacci matrix, G p,h,g , (p = 0, 1, 2, 3, • • • ), h(x) (> 0), g(y) (> 0) coincide with the relations among the code matrix for all values of p and h(x) = m(> 0) and g(y) = t(> 0) [8]. Also, the relations among the code matrix elements for h(x) = 1 and g(y) = 1, coincide with the generalized relations among the code matrix elements for Fibonacci coding theory [6]. By suitable selection for the initial terms in (h(x), g(y))-extension of the Fibonacci p-numbers, a new Fibonacci matrix, G p,h,g is applicable for Fibonacci coding/decoding. The correct ability of this method, increases as p increases but it is independent of h(x) and g(y). But h(x) and g(y) being polynomials, improves the cryptography protection. And complexity of this method increases as the degree of the polynomials h(x) and g(y) increases. We have also find a relation among golden (p, h(x), g(y))-proportion, golden (p, h(x))-proportion and golden p-proportion.

show abstract

Section: Introductionmentioning

confidence: 99%

Coding theory on (h(x); g(y))-extension of Fibonacci p-numbers polynomials

Prasad¹

2014

ujcmj

View full text Add to dashboard Cite

show abstract

“…It has also applications in physics [6,7,9], coding and information theory [1,10,23]. de Spinadel [5], Kappraff [15], Gazale [13] etc.…”

Section: Introductionmentioning

confidence: 99%

CODING THEORY ON THE (m, t)-EXTENSION OF THE FIBONACCI p-NUMBERS

Basu

Prasad²

2011

Discrete Math. Algorithm. Appl.

View full text Add to dashboard Cite

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 Fractals 42 (2009) 2522-2530.

show abstract

“…It has been shown that geometric, quasi-geometric, Fibonacci, exponential, Poisson and negative binomial distributions lie in the class of AUH sources for some regimes of their parameters [7], [18], [19], [20]. Related topic was addressed in [21], where the authors studied weakly super increasing (WSI) and partial WSI sources in connection with Fibonacci numbers and golden mean, which appeared extensively in modern science and, in particular, have applications in coding and information theory. 4 The rest of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Entropy and Average Cost of AUH Codes

Munteanu¹,

Tărniceriu²,

Zaharia³

2013

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

Abstract-In this paper we address the class of anti-uniform Huffman (AUH) codes, named also unary codes, for sources with finite and infinite alphabet, respectively. Geometric, quasi-geometric, Fibonacci, exponential, Poisson, and negative binomial distributions lead to anti -uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that as result of this encoding, in general, sources with memory are obtained. For these sources we attach the graph and determine the transition matrix between states, the state probabilities and the entropy. If c 0 and c 1 denote the costs for storing or transmission of symbols "0" and "1", respectively, we compute the average cost for these AUH codes.

show abstract

The Golden mean, Fibonacci matrices and partial weakly super-increasing sources

Cited by 10 publications

References 15 publications

Coding theory on (h(x); g(y))-extension of Fibonacci p-numbers polynomials

Coding theory on (h(x); g(y))-extension of Fibonacci p-numbers polynomials

CODING THEORY ON THE (m, t)-EXTENSION OF THE FIBONACCI p-NUMBERS

Entropy and Average Cost of AUH Codes

Contact Info

Product

Resources

About