Research Article of Research Journal of Mathematics and Computer Science
Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z
Dr. Ahmad Hamza Al Cheikha
Dep. of Mathematical Science, College of Arts-science and Education, Ahlia Uni., 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/pmZ, where Z is the integers and p is prime, replacing each event number by zero and replacing each odd number by one.
Keywords: Walsh Sequences, M-sequences, Additive group, Coefficient of Correlation, Orthogonal sequences, Quotient ring.
How to cite this article:
Ahmad Hamza Al Cheikha.Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z. Research Journal of Mathematics and Computer Science, 2018; 2:11.
 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.“Instant Walsh Functions” , SIAM Review., Vol. 12 1970, pp.131.
 David, J., “Introductory Modern Algebra, ”Clark University USA, 2008.
 Jong-Seon No, Solomon W. & Golomb,“ Binary Pseudorandom Sequences For period 2n-1 with Ideal Autocorrelation,”IEEE Trans. Information Theory, Vol.44 No 2,1998, PP 814-817.
 Lee J.S &Miller L.E, ”CDMA System Engineering Hand Book, ”Artech House. Boston, London,1998.
 Lidl, R.& Pilz,G., ”Applied Abstract Algebra,” Springer–Verlage New York, 1984.
 Lidl, R.& Nidereiter, H., “Introduction to Finite Fields and Their Application,” Cambridge University USA, 1994.
 Mac Wiliams, F.G& Sloane, N.G.A., “The Theory of Error- Correcting Codes,” North-Holland, Amsterdam, 2006.
 Sloane, N.J.A., “An Analysis Of The Stricture and Complexity Of Nonlinear Binary Sequence Generators,” IEEE Trans. Information Theory Vol. It 22 No 6,1976,PP 732-736.
 Thomson W. Judson, “Abstract Algebra: Theory and Applications , ” Free Software Foundation,2013.
 Yang S.C,”CDMA RF System Engineering, ”ArtechHouse.Boston-London,1998.
 Sakrison D.J. Communication Theory: Transmission of Waveforms and Digital information, Publisher: John Wiley & Sons Inc, 1968