## Shift Register Sequences |

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### Contents

The Present Status of the Shift Register Art | 2 |

Sequences With Randomness Properties | 24 |

Structural Properties of PN Sequences | 75 |

Copyright | |

27 other sections not shown

### Common terms and phrases

auto-correlation Boolean functions Bruijn sequences Chapter characteristic polynomial CM CM complementation compute condition corresponding Cycle Length Tap cycles of length cyclotomic cosets cyclotomic polynomial decomposition digits distinct divides equation equivalent example expected length feedback logic finite state machine formula given input sequence integer irreducible polynomials Lemma Length Tap Combina linear logic linear shift register longest cycle maximum exponent maximum-length shift register Mersenne prime method mmi mmi mmi modulo multiplicative node nonlinear shift register number of 1's number of cycles occurs order invariants permutation phase shift PN sequences polynomials of degree possible prime Proof properties recurrence relation roots of unity satisfies Section sequences of degree sequences of length shift register sequences shown in Figure subgroup successor tap combinations Theorem theory tion Cycle Length total number trinomial truth table tube variables vector diagram w-stage shift register xn-i