International Journal of Wireless Communications and Mobile Computing
Volume 8, Issue 1, June 2020, Pages: 9-17
Received: Jul. 17, 2020;
Accepted: Sep. 27, 2020;
Published: Oct. 14, 2020
Views 163 Downloads 32
Ahmad Hamza Al Cheikha, Department of Mathematical Science, College of Arts-science and Education, Ahlia University, Manama, Bahrain
Orthogonal Sequences (as M-Sequences, Walsh Sequences,…) are used widely at the forward links of communication channels to mix the information on connecting to and at the backward links of these channels to sift through this information is transmitted to reach the receivers this information in a correct form, especially in the pilot channels, the Sync channels, and the Traffic channel. This research is useful to generate new sets of orthogonal sequences (with the bigger lengths and the bigger minimum distance that assists to increase secrecy of these information and increase the possibility of correcting mistakes resulting in the channels of communication) from quotient rings Z/nZ, where Z is the integers and n is not of the form pm, where p is prime, replacing each event number by zero and each odd number by one, also, the increase in the natural number does not necessarily lead to an increase in the size of the biggest orthogonal set in the corresponding quotient ring. The length of any sequence in a biggest orthogonal set in the quotient ring Z/nZ is n and the minimum distance is between (n-3)/2 and (n-1)/2 and the sequences can be used as keywords or passwords for secret messages.
Ahmad Hamza Al Cheikha,
New Orthogonal Binary Sequences Using Quotient Rings Z/nZ Where n Is a Multiple of Some Prime Numbers, International Journal of Wireless Communications and Mobile Computing.
Vol. 8, No. 1,
2020, pp. 9-17.
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sakrison D. J., (1968), Communication Theory: Transmission of Waveforms and Digital information, Publisher: John Wiley & Sons Inc.
Al Cheikha A. H. (July, 2017). Compose M-Sequences. Australian Journal of Business, Social Science and Information Technology. AJBSSIT. Vol. 3, Issue 3. Pp. 119-126.
Al Cheikha A. H. (2017). Compose Binary Matrices. American Journal of Computer sciences and Applications. AJCSA. Vol. 1, Issue 2. Pp. 0001-0017.
Al Cheikha A. H. (September, 2014). Some Properties of M-Sequences Over Finite Field Fp. International Journal of Computer Engineering & Technology. IJCER. Vol. 5, Issue 9. Pp. 61-72.
Al Cheikha A. H. (September, 2014). Composed Walsh Sequences and M-Sequences. International Journal of Computers & Technology. IJCT. Vol. 15, Issue 7. Pp. 6933-6939.
Al Cheikha A. H. (2017). Composed Reed Solomon Sequences Generated by ith Partial Sum of Geometrical Sequences. American Journal of Computer sciences and Applications. AJCSA. Vol. 1, Issue 1. Pp. 0001-000116.
Byrnes, J. S.; Swick. (1970), “Instant Walsh Functions”, SIAM Review., Vol. 12, pp. 131.
David, J., “Introductory Modern Algebra,” Clark University, USA, 2008.
Jong-Seon No, Solomon W. & Golomb, (1998), “Binary Pseudorandom Sequences For period 2n-1 with Ideal Autocorrelation. IEEE Trans. Information Theory”, Vol. 44 No 2, PP 814-817.
Lee J. S & Miller L. E, (1998), “CDMA System Engineering Hand Book”, Artech House. Boston, London.
Lidl, R. & Pilz, G., (1984), ”Applied Abstract Algebra”, Springer–Verlage New York.
Lidl, R. & Nidereiter, H., (1994), “Introduction to Finite Fields and Their Application”, Cambridge University USA.
Al Cheikha A. H. (2018). Generating New Binary Sequences Using Quotient Rings Z/pmZ, Research Journal of Mathematics and Computer Science, RJMCS, ISSN: 2576-3989, Vol. 2 Issue 11. Pp. 1-13.
Mac Williams, F. G & Sloane, N. G. A., (2006), “The Theory of Error-Correcting Codes”, North-Holland, Amsterdam.
Sloane, N. J. A., (1976), “An Analysis Of The Stricture and Complexity Of Nonlinear Binary Sequence Generators, IEEE Trans. Information Theory” Vol. It 22 No 6, PP 732-736.
Thomson W. Judson, (2013), “Abstract Algebra: Theory and Applications”, Free Software Foundation.
Yang S. C, (1998), “CDMA RF System Engineering”, ArtechHouse. Boston-London.