A variant of the Narayana coding scheme

• Autorzy: Das Monojit , Sinha Sudipta
• Języki publikacji: EN

Abstrakty

EN

In this paper we use second order variant of the Narayana sequence to frame a universal coding scheme. Earlier, the Narayana series has been used by Kirthi and Kak to represent universal coding. This paper provides an extension, based on the paper by Kirthi and Kak. The second order variant Narayana universal coding is used in source coding as well as in cryptography.

Słowa kluczowe

EN

Fibonacci sequence; Zeckendorf’s representation; Narayana sequence; universal code; Narayana code straight line

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 3
• Strony: 473--484
• Opis fizyczny: Bibliogr. 17 poz., tab.

Twórcy

autor

Das Monojit

• Department of Mathematics, Shibpur Dinobundhoo Institution (College), 711 102 Howrah, W.B., India

autor

Sinha Sudipta

• Department of Mathematics, Burdwan Raj College, 713 104 Burdwan, W.B., India

Bibliografia

• Agarwal, P., Agarwal, N. and Saxena, R. (2015) Data Encryption through Fibonacci Sequence and Unicode Characters. MIT International Journal of Computer Science and Information Technology 5(2), 79-82.
• Basu, M. and Prasad, B. (2010) Long range variations on the Fibonacci universal code. Journal of Number Theory 130, 1925-1931.
• Buschmann, T. and Bystrykh, L. V. (2013) Levenshtein error-correcting barcodes for multiplexed DNA sequencing. BMC Bioinformatics 14(1), 272.
• Daykin, D. E. (1960) Representation of natural numbers as sums of generalized Fibonacci numbers. J. Lond. Math. Soc. 35, 143-160.
• Dubey, R., Verma, J. and Gaur, R. D. (2017) Encryption and Decryption of Data by Genetic Algorithm. International Journal of Scientific Research in Computer Science and Engineering 5(3), 47-52.
• Elias, P. (1975) Universal codeword sets and representations of the integers. IEEE Trans. Inform. Theory IT 21(2), 194-203.
• Filmus, Y. (2013) Universal codes of the natural numbers. Logical Methods in Computer Science 9(3:7), 111.
• Gupta, V., Singh, G. and Gupta, R. (2012) Advanced cryptography algorithm for improving data security. International Journal of Advanced Research in Computer Science and Software Engineering 2(1), 1-6.
• Kak, S. and Chatterjee, A. (1981) On decimal sequences. IEEE Trans. on Information Theory IT 27, 647–652.
• Kirthi, K. and Kak, S. (2016) The Narayana Universal Code. arxiv:1601. 07110.
• Malvar, H. S. (2006) Adaptive Run-Length/Golomb-Rice encoding of quantized generalized Gaussian sources with unknown statistics. http://re–search-srv.microsoft.com/ pubs/ 102069/ Malvar DCC06.pdf.
• Mukherjee, M. and Samanta, D. (2014) Fibonacci Based Text Hiding Using Image Cryptography. Lecture Notes on Information Theory 2(2), doi: 10.12720/lnit.2.2, 172-176.
• Platos, J., Baca, R., Snasel, V., Kratky, M. and El-Qawasmeh, E. (2007) The Fast Fibonacci encoding algorithm. arXiv: cs/0712.0811v2.
• Raphael, A. J. and Sundaram, V. (2012) Secured Communication through Fibonacci Numbers and Unicode Symbols. International Journal of Scientific & Engineering Research 3(4), 1-5.
• Singh, B., Sisodaya, K. and Ahmed, F. (2014) On the products of k-Fibonacci numbers and k-Lucas numbers. International Journal of Mathematics and Mathematical Sciences, Article ID 505798, 21, 1-4.
• Thomas, J. H. (2007) Variation on the Fibonacci universal code. arXiv:cs/0701085v2.
• Zeckendorf, E. (1972) Representation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Roy. Sci. Liége 41, 179-182

Uwagi

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