Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right. We extend the definition of SEDF from abelian groups to all finite groups, and introduce the concept of equivalence. We prove new recursive constructions for SEDFs and generalized SEDFs (GSEDFs) in cyclic groups, and present the first family of non-abelian SEDFs. We prove there exist at least two non-equivalent (k² + 1,2,k,1)-SEDFs for every k > 2, and begin the task of enumerating SEDFs, via a computational approach which yields complete results for all groups up to order 24.

中文翻译：

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阿拉伯和非阿拉伯群体中强大的外部差异家庭

强大的外部差异家族（SEDF）可应用于密码学，并且本身具有丰富的组合结构。我们将SEDF的定义从阿贝尔群扩展到所有有限群，并引入等价概念。我们证明了循环群中SEDF和广义SEDF（GSEDF）的新递归构造，并提出了非阿贝尔SEDF的第一个族。我们证明对于每个k > 2，至少存在两个非等价（k ² + 1,2，k，1）-SEDF ，并通过计算方法开始枚举SEDF的任务，该方法可得出所有组的完整结果订购24。