New constructions for disjoint partial difference families and external partial difference families
New constructions for disjoint partial difference families and external partial difference families
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DOI：
10.1002/jcd.21930
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发表时间：
2023-05
影响因子：
0.7
通讯作者：
Sophie Huczynska;Laura Johnson
中科院分区：
文献类型：
--
作者：
Sophie Huczynska;Laura Johnson
近年来，引入了一种新的组合结构，即不相交偏差族（DPDFs）和外部偏差族（EPDFs），它们同时推广了偏差集、不相交差族和外部差族，并在信息安全领域得到了应用。到目前为止，所有已知的构造方法都是在有限域中使用环切开术。在有限域以外的结构（特别是循环群和非贝尔群）中，我们提出了第一个非分环无限族的dpdf，它们也是epdf。除了直接构造外，我们还提出了一种利用相对差分集（rds）构造DPDFs/EPDFs的方法；作为其中的一部分，我们展示了众所周知的Bose RDS结果如何扩展到DPDFs和EPDFs的非常自然的结构。
Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference families and external difference families, and have applications in information security. So far, all known construction methods have used cyclotomy in finite fields. We present the first noncyclotomic infinite families of DPDFs which are also EPDFs, in structures other than finite fields (in particular cyclic groups and nonabelian groups). As well as direct constructions, we present an approach to constructing DPDFs/EPDFs using relative difference sets (RDSs); as part of this, we demonstrate how the well‐known RDS result of Bose extends to a very natural construction for DPDFs and EPDFs.