标题： 关于弯函数数量的渐近下界 显示英文标题

标题： An asymptotic lower bound on the number of bent functions

摘要： 一个在$n$个变量上的布尔函数$f$被称为弯函数，如果其所有沃尔什系数的绝对值为$2^{n/2}$。 我们的主要结果是对布尔弯函数数量的新渐近下界。 它基于对弯函数的 Maiorana--McFarland 类型的修改以及对拉丁方和超立方体中横截集数量估计的最新进展。 我们证明的副产品是布尔超立方体划分为$2$维仿射和线性子空间的数目的对数的渐近性。 显示英文摘要

摘要： A Boolean function $f$ on $n$ variables is said to be a bent function if the absolute value of all its Walsh coefficients is $2^{n/2}$. Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modification of the Maiorana--McFarland family of bent functions and recent progress in the estimation of the number of transversals in latin squares and hypercubes. By-products of our proofs are the asymptotics of the logarithm of the numbers of partitions of the Boolean hypercube into $2$-dimensional affine and linear subspaces.