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The generalized relations among the code elements for Fibonacci coding theory

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  • Basu, Manjusri
  • Prasad, Bandhu

Abstract

We have considered a class of square Fibonacci matrix of order (p+1) whose elements are based on the Fibonacci p numbers with determinant equal to +1 or −1. There is a relation between Fibonacci numbers with initial terms which is known as cassini formula. Fibonacci series and the golden mean plays a very important role in the construction of a relatively new space–time theory, which is known as E-infinity theory. An original Fibonacci coding/decoding method follows from the Fibonacci matrices. There already exists a relation between the code matrix elements for the case p=1 [Stakhov AP. Fibonacci matrices, a generalization of the cassini formula and a new coding theory. Chaos, Solitons and Fractals 2006;30:56–66.]. In this paper, we have established generalized relations among the code matrix elements for all values of p. For p=2, the correct ability of the method is 99.80%. In general, correct ability of the method increases as p increases.

Suggested Citation

  • Basu, Manjusri & Prasad, Bandhu, 2009. "The generalized relations among the code elements for Fibonacci coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2517-2525.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2517-2525
    DOI: 10.1016/j.chaos.2008.09.030
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    References listed on IDEAS

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    1. El Naschie, M.S., 2007. "The Fibonacci code behind super strings and P-Branes. An answer to M. Kaku’s fundamental question," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 537-547.
    2. El Naschie, M.S., 2006. "Topics in the mathematical physics of E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 656-663.
    3. Stakhov, A.P., 2006. "Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 56-66.
    4. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.
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    Cited by:

    1. Flaut, Cristina & Savin, Diana, 2019. "Some remarks regarding l-elements defined in algebras obtained by the Cayley–Dickson process," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 112-116.
    2. Flaut, Cristina & Savin, Diana, 2018. "Some special number sequences obtained from a difference equation of degree three," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 67-71.
    3. Emanuele Bellini & Chiara Marcolla & Nadir Murru, 2021. "An Application of p -Fibonacci Error-Correcting Codes to Cryptography," Mathematics, MDPI, vol. 9(7), pages 1-17, April.
    4. Basu, Manjusri & Prasad, Bandhu, 2009. "Coding theory on the m-extension of the Fibonacci p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2522-2530.

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