Generalization of Multiplication M-Sequences over Fp and Its Reciprocal Sequences

Generalization of Multiplication M-Sequences over Fp and Its Reciprocal Sequences

DOI: https://doi.org/10.30564/jeisr.v3i2.3740

Abstract


Mp-Sequences or M-Sequence over Fp not used so much in current time as binary M-Sequences and it is pending with the difficult to construct there coders and decoders of Mp-Sequences further these reasons there is expensive values to construct them but the progress in the technical methods will be lead to fast using these sequences in different life’s ways, and these sequences give more collection of information and distribution them on the input and output links of the communication channels, building new systems with more complexity, larger period, and security. In current article we will study the construction of the multiplication Mp-Sequence {zn}and its linear equivalent, this sequences are as multiple two sequences, the first sequence{Sn}is an arbitrary Mp-Sequence and the second sequence {ζn} reciprocal sequence of the first sequence {Sn}, length of the sequence {zn}, period, orthogonal and the relations between the coefficients and roots of the characteristic polynomial of f(x) and it’s reciprocal polynomial g(x) and compare these properties with corresponding properties in M-Sequences.


Keywords


Mp-Sequences; Finite fields; Shift register; Orthogonal; Complexity; Characteristic polynomial; Reciprocal polynomial

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