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New Orthogonal Binary Sequences Using Quotient Rings Z/nZ Where n Is a Multiple of Some Prime Numbers
International Journal of Wireless Communications and Mobile Computing
Volume 8, Issue 1, June 2020, Pages: 9-17
Received: Jul. 17, 2020; Accepted: Sep. 27, 2020; Published: Oct. 14, 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
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/nZ, where Z is the integers and n is not of the form pm, where p is prime, replacing each event number by zero and each odd number by one, also, the increase in the natural number does not necessarily lead to an increase in the size of the biggest orthogonal set in the corresponding quotient ring. The length of any sequence in a biggest orthogonal set in the quotient ring Z/nZ is n and the minimum distance is between (n-3)/2 and (n-1)/2 and the sequences can be used as keywords or passwords for secret messages.
Keywords
Walsh Sequences, M-sequences, Additive Group, Coefficient of Correlation, Orthogonal Sequences, Quotient Ring
Ahmad Hamza Al Cheikha, New Orthogonal Binary Sequences Using Quotient Rings Z/nZ Where n Is a Multiple of Some Prime Numbers, International Journal of Wireless Communications and Mobile Computing. Vol. 8, No. 1, 2020, pp. 9-17. doi: 10.11648/j.wcmc.20200801.12
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