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Volume 13, Issue 1
A New Coding Theory on Fibonacci n-Step Polynomials

Monojit Das and Manjusri Basu

J. Info. Comput. Sci. , 13 (2018), pp. 056-073.

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  • Abstract
In this paper, we develop a new series of Fibonacci ?-step polynomials. Based on these series of polynomials, we introduce a new class of square matrix of order ?. Thereby, we define a new coding theory called Fibonacci ?-step polynomials coding theory. Then we calculate the generalized relations among the code elements for all values of ?. It is shown that, for ? = 2, the correct ability of this method is 93.33% whereas for n = 3, the correct ability of this method is 99.80%. The interesting part of this coding/decoding method is that the correct ability does not depend on ? and increases as ? increases.
  • Keywords

Fibonacci numbers, Fibonacci n-step numbers, Fibonacci polynomials, Fibonacci n-step polynomials, Fibonacci n-step polynomials coding, Error correction.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JICS-13-056, author = {Monojit Das and Manjusri Basu}, title = {A New Coding Theory on Fibonacci n-Step Polynomials}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {13}, number = {1}, pages = {056--073}, abstract = {In this paper, we develop a new series of Fibonacci ?-step polynomials. Based on these series of polynomials, we introduce a new class of square matrix of order ?. Thereby, we define a new coding theory called Fibonacci ?-step polynomials coding theory. Then we calculate the generalized relations among the code elements for all values of ?. It is shown that, for ? = 2, the correct ability of this method is 93.33% whereas for n = 3, the correct ability of this method is 99.80%. The interesting part of this coding/decoding method is that the correct ability does not depend on ? and increases as ? increases. }, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22464.html} }
TY - JOUR T1 - A New Coding Theory on Fibonacci n-Step Polynomials AU - Monojit Das and Manjusri Basu JO - Journal of Information and Computing Science VL - 1 SP - 056 EP - 073 PY - 2024 DA - 2024/01 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22464.html KW - Fibonacci numbers, Fibonacci n-step numbers, Fibonacci polynomials, Fibonacci n-step polynomials, Fibonacci n-step polynomials coding, Error correction. AB - In this paper, we develop a new series of Fibonacci ?-step polynomials. Based on these series of polynomials, we introduce a new class of square matrix of order ?. Thereby, we define a new coding theory called Fibonacci ?-step polynomials coding theory. Then we calculate the generalized relations among the code elements for all values of ?. It is shown that, for ? = 2, the correct ability of this method is 93.33% whereas for n = 3, the correct ability of this method is 99.80%. The interesting part of this coding/decoding method is that the correct ability does not depend on ? and increases as ? increases.
Monojit Das and Manjusri Basu. (2024). A New Coding Theory on Fibonacci n-Step Polynomials. Journal of Information and Computing Science. 13 (1). 056-073. doi:
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