ON THE NONEXISTENCE of BENT FUNCTIONS
Yin Zhang, Meicheng Liu, Dongdai Lin · International Journal of Foundations of Computer Science · 2011
In this paper, we study the nonexistence of bent functions in the class of Boolean functions without monomials of degree less than d in their algebraic normal forms (ANF). We prove that n-variable Boolean functions in such class are not bent when there are not more than n + d - 3 monomials in their ANFs. We also show that an n-variable Boolean function is not bent if it has no monomial of degree less than ⌈3n/8 + 3/4⌉ in its ANF.