On h(x) Lucas polynomials with application to coding

• Autorzy: Prasad Bandhu
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the h(x) Lucas polynomials of order m and the Un matrix, whose elements are Lucas polynomials, h(x)(> 0) being a polynomial with real coefficients. We also establish the relations among the code matrix elements.

Słowa kluczowe

EN

Lucas numbers; Lucas polynomials; golden mean; code matrix

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 4
• Strony: 557--573
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Prasad Bandhu

• Department of Mathematics, Kandi Raj College, Kandi - 742137, India

Bibliografia

• Basu, M. and Prasad, B. (2009) The generalized relations among the code elements for Fibonacci coding theory. Chaos, Solitons and Fractals, 41, 2517-2525.
• Blahut, R. (1983) The Theory and Practice of Error Control Codes. Addison-Wesley, Reading, MA.
• Cover, T.M. and Thomas, J.A.(1991) Elements of Information Theory. A Wiley-Interscience Publication. New York
• El Naschie, M.S. (2009) The theory of Cantorian space time and high energy particle physics. Chaos, Solitons and Fractals, 41, 2635-2646.
• Esmaeeili, M., Gulliver, T.A. and Kakhbod, A. (2009) The Golden mean, Fibonacci matrices and partial weakly super-increasing sources. Chaos, Solitons and Fractals, 42, 435-440.
• Hohn, F.E. (1973) Elementary Matrix Algebra. Macmillan Company, New York.
• MacWilliams, F.J. and Sloane, N.J.A. (1977) Theory of Error-Correcting Codes. North-Holland. Amsterdam
• Nalli, A. and Haukkanen, P. (2009) On generalized Fibonacci and Lacus polynomials. Chaos, Solitons and Fractals, 42, 3179-3186.
• Prasad, B. (2015) Coding theory on h(x) extension of m sequences for Fibonacci numbers. Discrete Mathematics, Algorithms and Applications, 7, 2, 1550008 (18 pages).
• Prasad, B. (2016) Coding theory on Lucas p-numbers. Discrete Mathematics, Algorithms and Applications, 8, 4, 1650074 (17 pages).
• Prasad, B. (2019) Corrigendum: Coding theory on the m-extension of the Fibonacci p -numbers. Chaos, Solitons and Fractals, Article in press.
• Stakhov, A.P. (1977) Introduction into algorithm measurement theory. Soviet Radio, Moscow (In Russian).
• Stakhov, A.P. (2006) Fibonacci matrices, a generalization of the cassini formula and a new coding theory. Chaos, Solitons and Fractals, 30, 56-66.
• Tasci, D. and Kilic, E. (2004) On the order k generalized Lucas numbers. Appl Math Comput, 155, 637-641.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).