Utilizing m sequence shift register to create pseudorandom sequences is one critical method to construct desired sequences. In this thesis, a new type of nonlinear m subsequence is proposed through the analysis of feedback function of m sequence shift register with three items' primary polynomial. Eigenfunction of m subsequence shift register is presented. A new method to construct feedback function of nonlinear m subsequence based on root function is also presented. Through the feedback functions, the nonlinear maximal length pseudorandom sequences are realized on FPGA. Meanwhile, the corresponding analysis demonstrates that this type of sequence has ideal pseudorandom characteristic and desirable linear complexity.
The M-Sequences have been widely used in many areas such as telecommunication, cryptology, navigation and radar. Due to the difficulties of constructing the feedback functions of M-sequences, a new method of constructing one class M-sequence and its feedback function were presented. A sub-function Y was formed by remodeling the M root-sequence states diagram. To affix sub-function y to the feedback function f M of M root-sequence, a new class M-sequence feedback function f' M was obtained. Meanwhile, the corresponding analysis demonstrates that this type of sequence has the desirable pseudorandom characteristic. The sequences are realized in practice and proved to be satisfactory and desirable.
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