论文标题
薄的sidon集和矢量布尔函数的非线性
Thin Sidon sets and the nonlinearity of vectorial Boolean functions
论文作者
论文摘要
向量值函数的矢量非线性是其与仿射函数集的距离。 2017年，刘，梅斯纳格和陈猜想了矢量线性的一般上限。最近，在差异均匀性方面，阵阵被证明是一个下限。在本文中，我们改善了行李的下限。我们的方法是基本的，它依赖于以下事实：APN函数的级别集是Sidon集。我们对基础Abelian 2组中的Sidon集进行了调查。我们研究从有限仿射平面的双曲线和椭圆的Sidon集的完整性问题。
The vectorial nonlinearity of a vector valued function is its distance from the set of affine functions. In 2017, Liu, Mesnager and Chen conjectured a general upper bound for the vectorial linearity. Recently, Carlet proved a lower bound in terms of the differential uniformity. In this paper, we improve Carlet's lower bound. Our method is elementary, it relies on the fact that the level sets of an APN functions are Sidon sets. We give a survey on Sidon sets in elementary abelian 2-groups. We study the completeness problem of Sidon sets obtained from hyperbolas and ellipses of the finite affine plane.
