Goresky M., Klapper A. Algebraic Shift Register Sequences

Cambridge University Press, 2012. — 515.Pseudo-random sequences are essential ingredients of every modern digital communication system, from cellular telephones to satellite imagery. This book describes the design, mathematical analysis and implementation of pseudo-random sequences. Suitable for graduate students of mathematics or electrical engineering, it also serves as a reference book for researchers in the field.Part I Algebraically Defined Sequences
Sequences
Linear feedback shift registers and linear recurrences
Feedback with carry shift registers and multiply with carry sequences
Algebraic feedback shift registers
d-FCSRs
Galois mode, linear registers, and related circuits
Part II Pseudo-Random and Pseudo-Noise Sequences
Measures of pseudo-randomness
Shift and add sequences
m-sequences
Related sequences and their correlations
Maximal period function field sequences
Maximal period FCSR sequences
Maximal period d-FCSR sequences
Part III Register Synthesis and Security Measures
Register synthesis and LFSR synthesis
FCSR synthesis
AFSR synthesis
Average and asymptotic behavior of security measures
Part IV Algebraic Background
A: Abstract algebra
B: Fields
C: Finite local rings and Galois rings
D: Algebraic realizations of sequences