Compose Quotient Ring Sequences With Walsh’s Sequences and M-Sequences

Compose Quotient Ring Sequences With Walsh’s Sequences and M-Sequences

Ahmad Hamza Al Cheikha

Dep. of Mathematical Science, College of Arts-science and Education

American Journal of Computer Engineering

Orthogonal sequences as Walsh Sequences, M-Sequences and other sequences 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 correct form, specially in the pilot channels, the Sync channels, and the Traffic channel.
This research is useful to generate new orthogonal sets of sequences (which are also with the corresponding null sequence additive groups) by compose quotient ring sequences with the best and very important orthogonal sequences, Walsh sequences and M-sequences, and by inverse, 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.

Keywords: Quotient ring Sequences, Walsh Sequences, M-sequences, Coefficient of Correlation, Code, Orthogonal sequences, Additive group, Span.

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How to cite this article:
Ahmad Hamza Al Cheikha. Compose Quotient Ring Sequences With Walsh’s Sequences and M-Sequences. American Journal of Computer Engineering, 2019; 2:4.

[1]. Al Cheikha A. H. (2018; 2:11), “Generating new binary orthogonal sequences using quotient rings Z/pmZ”, Research Journal of Mathematics and Computer Science (RJMCS), pp 1-13.
[2]. Al Cheikha A. H.(2016), “Compose Walsh’s Sequences and M-Sequences”, International journal of computer and technology (IJCT), Vol. 15, No. 7, 2016. pp. 6933- 6939.
[3]. Al Cheikha A. H. (2005), “Isomorphic Sequences Sets Generation of the Walsh Sequences”, Qatar University Science Journal Vol. 25, 2005. pp. 16-30.
[4]. Byrnes, J.S., Swick, D. A. (1970),“Instant Walsh Functions”,( SIAM Review., Vol. 12, pp.131.
[5]. Yang S.C,(1998),”CDMA RF System Engineering,” Boston, London: Artech House.
[6]. Thomson, J.T. (2013), “Abstract Algebra: Theory and Applications,” Free Software Foundation.
[7]. Lidl, R., Pilz, G. (1984), “Applied Abstract Algebra”, New York: Springer-Verlage New York.
[8]. Mac Williams, F.G., Sloane, G.A. (2006), The Theory of Error-Correcting Codes. Amsterdam: North-Holland
[9]. Lidl, R., Nidereiter, H. (1994), “Introduction to Finite Fields and Their Application,”Cambridge University USA,.
[10]. Sloane, N.J.A. (1076),“An Analysis Of The Stricture and Complexity Of Nonlinear Binary Sequence Generators,” IEEE Trans. Information Theory Vol. It 22, No 6, PP 732- 736.
[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. (Australia and New Zealand Business and Social Science Research Conference (ANZBSRC) 2016).
[12]. Jong, N.S., Golomb, S.W., Gong, G., Lee, H.K., Gaal, P. (1998), “ Binary Pseudorandom For period 2n-1 with Ideal Autocorrelation, ”IEEE Trans. Information Theory, Vol. 44 No 2, PP. 814-817
[13]. Lee, J.S., Miller, L.E. (1998), CDMA System Engineering Hand Book. Boston, London: Artech House.
[14]. Yang, K., Kim, Y.K., Kumar, P.V. (2000), “Quasi–orthogonal Sequences for code –Division Multiple Access Systems ,“IEEE Trans .information theory, Vol. 46 No3, 982- 993,.
[15]. Farleigh, J.B. (1971), “A First course In Abstract Algebra, Fourth printing. Addison- Wesley publishing company USA.
[16]. Al Cheikha A. H., Ruchin J. (March , (2014), “Generation of Orthogonal Sequences by Walsh Sequences” International Journal of Soft Computing and Engineering Vol.4, Issue- 1, pp. 182-184.
[17]. Al Cheikha A. H. ( 30th December 2015 ),“Compose Walsh’s Sequences and Reed Solomon Sequences”, ISERD International Conference, Cairo, Egypt, ISBN: 978-93- 85832-90-1, pp. 23-26.
[18]. Kacami, T., Tokora, H. (1978), “Teoria Kodirovania”, MOSCOW: Mir.
[19]. David, J. (2008 ),“Introductory Modern Algebra, ”Clark University USA.