Study the Linear Equivalent of the Binary Nonlinear Sequences
International Journal of Information and Communication Sciences
Volume 5, Issue 3, September 2020, Pages: 24-39
Received: Jul. 8, 2020; Accepted: Jul. 28, 2020; Published: Aug. 27, 2020
Views 56      Downloads 17
Author
Ahmad Hamza Al Cheikha, Department of Mathematical Science, College of Arts-science and Education, Ahlia University, Manama, Bahrain
Article Tools
Follow on us
Abstract
Linear orthogonal sequences, special M-Sequences, are used widely in the systems communication channels as in the forward links for mixing the information on connection and as in the backward links of these channels to sift this information which transmitted and the receivers get the information in a correct form. In current research trying to study the construction of the linear equivalent of a multiplication sequence and answering on the question "why the length of the linear equivalent of a multiplication sequence (on a linear M-sequence{an}), in some cases doesn't reach the maximum length rNh, special, when the multiplication is on three or more degrees of the basic sequence {an} The multiplication sequence has high complexity and the same period of the basic sequence, or if the multiplication sequence on two different basic sequences then the period of multiplication sequence is equal to multiplication the two periods of the basic sequences, and in the two cases the multiplication sequence is not an orthogonal sequence.
Keywords
Linear Sequences, Finite Field, Linear Feedback Shift Register, Orthogonal Sequence, Linear Equivalent, Complexity
To cite this article
Ahmad Hamza Al Cheikha, Study the Linear Equivalent of the Binary Nonlinear Sequences, International Journal of Information and Communication Sciences. Vol. 5, No. 3, 2020, pp. 24-39. doi: 10.11648/j.ijics.20200503.11
Copyright
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.
References
[1]
Yang K, Kg Kim y Kumar l. d, (2000), “Quasi–orthogonal Sequences for code –Division Multiple Access Systems, “IEEE Trans. information theory, Vol. 46, No3, PP 982-993.
[2]
Jong-Seon No, Solomon W. & Golomb, (1998), “Binary Pseudorandom Sequences For period 2n-1with Ideal Autocorrelation”, IEEE Trans. Information Theory, Vol. 44 No 2, PP 814-817.
[3]
Golamb S. W. (1976), Shift Register Sequences, San Francisco – Holden Day.
[4]
Lee J. S & Miller L. E, (1998), “CDMA System Engineering Hand Book,” Artech House. Boston, London.
[5]
Yang S. C, “CDMA RF, (1998), System Engineering,”Artech House. Boston- London.
[6]
Mac Wiliams, F. G & Sloane, N. G. A., (2006), “The Theory of Error- Correcting Codes,” North-Holland, Amsterdam.
[7]
Kasami, T. & Tokora, H., (1978), “Teoria Kodirovania,” Mir (Moscow).
[8]
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.
[9]
Al Cheikha A. H. (May 2014), “ Matrix Representation of Groups in the finite Fields GF(pn),”International Journal of Soft Computing and Engineering, Vol. 4, Issue 2, PP 118-125.
[10]
Lidl, R. & Pilz, G., (1984), “Applied Abstract Algebra,” Springer – Verlage New York, 1984.
[11]
Lidl, R. & Niderreiter, H., (1994), “Introduction to Finite Fields and Their Application,” Cambridge university USA.
[12]
Thomson W. Judson, (2013), “Abstract Algebra: Theory and Applications,” Free Software Foundation.
[13]
Fraleigh, J. B., (1971), “A First course In Abstract Algebra, Fourth printing. Addison- Wesley publishing company USA.
[14]
David, J., (2008), “Introductory Modern Algebra,” Clark University USA.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186