Study the Multiplication M-sequences and Its Reciprocal Sequences

Ahmad Al Cheikha; Ebtisam Haj Omar

doi:10.30564/jeisr.v3i1.3507

Study the Multiplication M-sequences and Its Reciprocal Sequences

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

Article ID: 3507

DOI: https://doi.org/10.30564/jeisr.v3i1.3507

Abstract

M-Sequences play a big important role, as the other binary orthogonalsequences, for collection the information on the input links and distributionthese information on the output links of the communication channelsand for building new systems with more complexity, larger period, andsecurity, through multiplication these sequences. In our article we try tostudy the construction of the multiplication sequence {zn}and its linearequivalent, this multiplication sequence is as multiple two sequences, thefirst sequence{an}is an arbitrary M-sequence and the second sequence{bn}is not completely different but is the reciprocal sequence of the firstsequence {an} that is the reciprocal sequence has characteristic polynomialg(x) is reciprocal of f(x), which is the characteristic polynomial of the firstsequence {an}, also we will study the linear equivalent of the multiplicationsequence {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

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