Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z

Generating New Orthogonal Binary Sequences Using Quotient Rings Z/pm Z

Dr. Ahmad Hamza Al Cheikha

Dep. of Mathematical Science, College of Arts-science and Education, Ahlia Uni., Manama, Bahrain

Research Journal of Mathematics and Computer Science

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/pmZ, where Z is the integers and p is prime, replacing each event number by zero and replacing each odd number by one.

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

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