PIMS - SFU Discrete Math Seminar: Xiang-dong Hou

Abstract: Two Boolean functions from $\Bbb F_2^n$ to $\Bbb F_2$ are called (affine) equivalent if one can be obtained from the other through an invertible affine transformation of the variables followed by an addition of an affine function. Most coding theoretic and cryptographic properties of Boolean functions are preserved under this equivalence. Let $N_n$ denote the number of equivalence classes of Boolean functions in $n$ variable. No explicit formula for $N_n$ is known. A long-standing open question by MacWilliams and Sloane asks for an asymptotic formula for $N_n$ as $n\to\infty$. Recently, we find a solution to this question.