## Shift Register Sequences: Secure And Limited-access Code Generators, Efficiency Code Generators, Prescribed Property Generators, Mathematical Models (Third Revised Edition)Shift register sequences cover a broad range of applications, from radar signal design, pseudo-random number generation, digital wireless telephony, and many other areas in coded communications. It is the primary area for which the author, Dr Golomb, received the US National Medal of Science. This book is the third, revised edition of the original definitive book on shift register sequences which was published in 1967, which has been widely distributed, read, and cited. It has stood the test of time, and provides a clear, comprehensive, and readily applicable description of both linear and non-linear shift register sequences. |

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### Contents

PART II THE LINEAR THEORY | 23 |

PART III THE NONLINEAR THEORY | 109 |

223 | |

Chapter IX Selective Update | 225 |

233 | |

### Common terms and phrases

auto-correlation Boolean functions Bruijn sequences Chapter characteristic polynomial Combination Length Combination complementation computed Cont'd corresponding cross-correlation Cycle containing cycle lengths Cycle Tap Cycle cycles of length cyclotomic cosets cyclotomic polynomial digits divides equation example expected length feedback logic finite state machine Group input sequence integer intentionally left blank irreducible polynomials Length Combination Length Length quency linear logic linear shift register longest cycle Mathematical maximum exponent maximum-length shift register Mersenne prime method modulo multiplicative n-stage shift register node nonlinear shift register number of 1's number of cycles occur Octal order invariants permutation phase shift PN sequences polynomials of degree Proof recurrence relation roots of unity satisfies Section sequences of degree sequences of length shift register sequences shown in Figure subgroup successor tap combinations Tap Cycle Tap Tap Tap Tap Theorem theory trinomials truth table variables