论文标题
弯曲功能的线性代码和发病率及其概括
Linear codes and incidence structures of bent functions and their generalizations
论文作者
论文摘要
在本文中，我们考虑了$（n，m）$的进一步应用，用于构建2设计。例如，我们通过证明APN的线性代码具有经典的WALSH Spectrum Spectrum支持的2-Designs来提供扩展Assmus-Mattson定理的新应用。另一方面，我们使用线性代码和组合设计来研究$（n，m）$函数的重要属性。特别是，我们给出了$（n，m）$ - 平台和$（n，m）$ - 弯曲函数的新设计理论表征，并提供了对$（n，m）$ - 弯曲功能的可扩展性问题的编码理论以及设计理论解释。
In this paper we consider further applications of $(n,m)$-functions for the construction of 2-designs. For instance, we provide a new application of the extended Assmus-Mattson theorem, by showing that linear codes of APN functions with the classical Walsh spectrum support 2-designs. On the other hand, we use linear codes and combinatorial designs in order to study important properties of $(n,m)$-functions. In particular, we give a new design-theoretic characterization of $(n,m)$-plateaued and $(n,m)$-bent functions and provide a coding-theoretic as well as a design-theoretic interpretation of the extendability problem for $(n,m)$-bent functions.
