Chapter 1

Boolean Functions

Abstract

In this chapter, we start with basic definitions related to Boolean functions. We consider the algebraic normal form of a Boolean function and the representation of a Boolean function over the Boolean cube. Extended affinely equivalent Boolean functions are defined as is the Walsh-Hadamard transform of a Boolean function. The finite field over F2si1_e and its automorphisms are considered. It is shown how to associate Boolean functions in n variables with functions over the field F2nsi2_e. We discuss polynomial representations ...

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