In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299–5309, 2020), when the initial function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for $$n=8$$ n = 8 and produces fifteen new APN functions for $$n=9$$ n = 9 .

中文翻译：

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APN 函数的广义同位素位移构造

在这项工作中，我们对 Budaghyan 等人最近引入的同位素位移构造进行了一些概括。(IEEE Trans Inform Theory 66:5299–5309, 2020)，当初始函数是 Gold 函数时。特别是，我们推导出了 APN 函数的一般构造，它涵盖了 $$n=8$$n = 8 的几个未分类的 APN 函数，并为 $$n=9$$n = 9 生成了 15 个新的 APN 函数。