Compose Quotient Ring Sequences with Walsh’s Sequences and M-Sequences
Issue:
Volume 5, Issue 1, February 2019
Pages:
10-20
Received:
7 December 2018
Accepted:
4 April 2019
Published:
6 May 2019
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.
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 lin...
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, 
and 
in the Category of A - Alg
a finitely presented right A-algebra and 
a (B-A)-bialgebra, then 
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, also 
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