In a recent work, Beierle, Brinkmann and Leander presented a recursive tree search for finding APN permutations with linear self-equivalences in small dimensions. In this short paper, we describe how this search can be adapted to find many new instances of quadratic APN functions. In particular, we found 12,923 new quadratic APN functions in dimension eight, 35 new quadratic APN functions in dimension nine and five new quadratic APN functions in dimension ten up to CCZ-equivalence. Remarkably, two of the 35 APN functions in dimension nine are APN permutations that have not been known before. Among the 8-bit APN functions, there are three extended Walsh spectra that were not known to be valid extended Walsh spectra of quadratic 8-bit APN functions before and, surprisingly, there exist at least four CCZ-inequivalent 8-bit APN functions with linearity $2^7$, i.e. the highest possible non-trivial linearity.

中文翻译：

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二次 APN 函数的新实例

在最近的一项工作中，Beierle、Brinkmann 和 Leander 提出了一种递归树搜索，用于在小维度中寻找具有线性自等价的 APN 排列。在这篇简短的论文中，我们描述了如何调整这种搜索以找到二次 APN 函数的许多新实例。特别是，我们在第 8 维发现了 12,923 个新的二次 APN 函数，在第 9 维发现了 35 个新的二次 APN 函数，在第 10 维发现了五个新的二次 APN 函数，直到 CCZ 等价。值得注意的是，第 9 维的 35 个 APN 函数中有两个是以前未知的 APN 排列。在 8 位 APN 函数中，有 3 个扩展的沃尔什谱，它们之前并不知道是二次 8 位 APN 函数的有效扩展沃尔什谱，而且令人惊讶的是，