Correlation functions: maximum-length sequences and their auto- and cross-correlation properties.Linear feedback shift registers: design of LFSRs based on Galois Field Theory, methods for searching primitive polynomials.Working with extension fields: representations of primitive polynomials, addition and multiplication over extension fields, methods to calculate multiplicative inverses.Galois and extension fields: modular arithmetic, definition of groups, rings and fields, definition and theorems on Galois and extension fields.This book is structured into the following chapters: The goal of this book is to build a bridge from the mathematics of Galois fields, in particular extension fields, toward the related circuit theory in terms of linear feedback shift registers and their usage in several technical applications. The design of such LFSRs is based on the mathematical theory of finite fields, the so-called Galois fields. Such sequences can easily be generated by linear feedback shift registers (LFSRs). ![]() Pseudo random sequences play a significant role in several technical areas, such as navigation systems or cryptography.
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