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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
Author
Ahmad Hamza Al Cheikha, Department of Mathematical Science, College of Arts-science and Education, Ahlia University, Manama, Bahrain
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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
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
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