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 F2 and its automorphisms are considered. It is shown how to associate Boolean functions in n variables with functions over the field F2n. We discuss polynomial representations of Boolean and vectorial Boolean functions. Representations of a Boolean function in the trace form and in the reduced trace form are given. Some details on the degree of a Boolean function in the trace form and on monomial functions are presented. The notions introduced in this chapter will be useful throughout the book.
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