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Study the Multiplication M-sequences and Its Reciprocal Sequences

Authors

  • Ahmad Al Cheikha Email Math. Sci.Dep., Ahlia Uni., Bahrain
  • Ebtisam Haj Omar Elect. Energy Dep., Tishreen Univ, Syria

DOI:

https://doi.org/10.30564/jeisr.v3i1.3507
Received: 2 August 2021 | Published Online: 23 August 2021

Abstract

M-Sequences play a big important role, as the other binary orthogonal
sequences, for collection the information on the input links and distribution
these information on the output links of the communication channels
and for building new systems with more complexity, larger period, and
security, through multiplication these sequences. In our article we try to
study the construction of the multiplication sequence {zn}and its linear
equivalent, this multiplication sequence is as multiple two sequences, the
first sequence{an}is an arbitrary M-sequence and the second sequence
{bn}is not completely different but is the reciprocal sequence of the first
sequence {an} that is the reciprocal sequence has characteristic polynomial
g(x) is reciprocal of f(x), which is the characteristic polynomial of the first
sequence {an}, also we will study the linear equivalent of the multiplication
sequence {zn}and we will see that the length of the linear equivalent of {zn}
is equal to ((deg f(x))2 - deg(f(x)).

Keywords:

Binary sequences, Finite fields, Shift register, Equivalent binary linear shift register, Degree of complexity

References

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Issue

2021 Vol.3 No.1

Article Type

Article

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Copyright © 2021 Ahmad Al Cheikha, Ebtisam Haj Omar

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