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

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  • Basu, Manjusri
  • Prasad, Bandhu

Abstract

In this paper, we introduce a new Fibonacci Gp,m matrix for the m-extension of the Fibonacci p-numbers where p (⩾0) is integer and m (>0). Thereby, we discuss various properties of Gp,m matrix and the coding theory followed from the Gp,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=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.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2522-2530
    DOI: 10.1016/j.chaos.2009.03.197
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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.
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    4. 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.
    5. El Naschie, M.S., 2006. "Topics in the mathematical physics of E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 656-663.
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    7. 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.
    8. Stakhov, A.P., 2007. "The “golden” matrices and a new kind of cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1138-1146.
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    Cited by:

    1. Prasad, Bandhu, 2020. "Corrigendum: Coding theory on the m-extension of the Fibonacci p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Ivana Matoušová & Pavel Trojovský, 2020. "On Coding by (2, q )-Distance Fibonacci Numbers," Mathematics, MDPI, vol. 8(11), pages 1-24, November.

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