Boolean functions play an important role in coding theory and symmetric cryptography. In this paper, three classes of Boolean functions with six-valued Walsh spectra are presented and their Walsh spectrum distributions are determined. They are derived from three classes of bent functions by complementing the values of the functions at three different points, where the bent functions are the Maiorana-McFarland types, Dillon \(\mathcal {PS}_{ap}\) types and the monomial form \(T{r^{n}_{1}}(\lambda x^{r(2^{m}-1)})\), respectively. As an application, we construct some classes of binary linear codes and it turns out that these codes can be used in secret sharing schemes with interesting access structure.

布尔函数在编码理论和对称密码学中起着重要作用。本文提出了三类具有六值沃尔什谱的布尔函数，并确定了它们的沃尔什谱分布。它们是通过对三个不同点的函数值进行补充而从三类弯曲函数派生而来的，其中弯曲函数为Maiorana-McFarland类型，Dillon \（\ mathcal {PS} _ {ap} \）类型和一项式分别为\（T {r ^ {n} _ {1}}（\ lambda x ^ {r（2 ^ {m} -1）}）\）形式。作为应用程序，我们构造了一些类别的二进制线性代码，结果证明这些代码可用于具有有趣访问结构的秘密共享方案中。