International Journal of Theoretical and Applied Mathematics
Volume 5, Issue 1, February 2019, Pages: 10-20
Received: Dec. 7, 2018;
Accepted: Apr. 4, 2019;
Published: May 6, 2019
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Ahmad Hamza Al Cheikha, Department of Mathematical Science, College of Arts-Science and Education, Ahlia University, Manama, Bahrain
Quotient ring sequences are completely new orthogonal sets without coders and decoders to the moment but Walsh sequences of the order 2k, k positive integer, and M-Sequences with zero sequence form additive groups, Except the zero sequences, Walsh sequences, and M-Sequences formed orthogonal sets and used widely in the forward links and inverse links of communication channels for mixing and sifting information as in the systems CDMA and other channels. The current paper studied the orthogonal sets (which are also with the corresponding null sequence additive groups) generated through compose quotient ring sequences with self, Compose quotient ring sequences with the best and very important sequences Walsh sequences and M-sequences and by inverse for getting these new orthogonal sets or sequences with longer lengths and longer minimum distances in order to increase the confidentiality of information and increase the possibility of correcting mistakes in the communication channels.
Ahmad Hamza Al Cheikha,
Compose Quotient Ring Sequences with Walsh’s Sequences and M-Sequences, International Journal of Theoretical and Applied Mathematics.
Vol. 5, No. 1,
2019, pp. 10-20.
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.
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.
Byrnes, J. S., Swick, D. A. (1970), “Instant Walsh Functions”, (SIAM Review., Vol. 12, pp.131.
Yang S. C, (1998),”CDMA RF System Engineering,” Boston, London Artech House.
Thomson, J. T. (2013), “Abstract Algebra Theory and Applications,” Free Software Foundation.
Al Cheikha A. H. (2005), “Isomorphic Sequences Sets Generation of the Walsh Sequences”, Qatar University Science Journal Vol. 25, 2005. pp. 16-30.
Lidl, R., Pilz, G. (1984), “Applied Abstract Algebra”, New York Springer-Verlage New York.
Mac Williams, F. G., Sloane, G. A. (2006), The Theory of Error-Correcting Codes. Amsterdam North-Holland.
Lidl, R., Nidereiter, H. (1994), “Introduction to Finite Fields and Their Application,” Cambridge University USA,.
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.
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.
Jong, N. S., Golomb, S. W., Gong, G., Lee, H. K., Gaal, P. (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. Boston, London Artech House.
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, Pp. 982- 993,.
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.
Kacami, T., Tokora, H. (1978), “Teoria Kodirovania”, MOSCOW: Mir.
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).
Farleigh, J. B. (1971), A First course In Abstract Algebra, Fourth printing. Addison-Wesley publishing company USA.
David, J. (2008), “Introductory Modern Algebra,” Clark University USA.