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Compose Quotient Ring Sequences with Walsh’s Sequences and M-Sequences
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
Author
Ahmad Hamza Al Cheikha, Department of Mathematical Science, College of Arts-Science and Education, Ahlia University, Manama, Bahrain
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Abstract
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.
Keywords
Quotient ring Sequences, Walsh Sequences, M-sequences, Coefficient of Correlation, Code, Orthogonal Sequences, Additive group, Span
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. doi: 10.11648/j.ijtam.20190501.12
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