论文标题
部分差异集
Packings of partial difference sets
论文作者
论文摘要
部分差异集的包装是有限组$ g $中的不相交部分差异集的集合。多年来，这种配置在设计理论，有限的几何形状，编码理论和图形论中受到了极大的关注，尽管通常只是隐式。我们考虑在具有相同参数的阿贝尔组中某些拉丁方形型部分差异集的包装，集合的大小是最大值或一个较小的。我们在一个共同的框架中统一并扩展了许多先前的结果，因为他们认识到特定的子组揭示了有关包装的重要结构信息。确定该亚组使我们能够在增加指数的阿贝尔群体中制定包装的递归提升，以及在起始组的直接产品中产生包装的产品构造。我们还研究亚伯群中某些负拉丁方形型部分差分差的包装，这些构成的最大大小的最大尺寸集除外，除其中一个都具有相同的参数，并展示了如何使用拉丁方形型部分差异集的包装来产生此类集合。
A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over many years, although often only implicitly. We consider packings of certain Latin square type partial difference sets in abelian groups having identical parameters, the size of the collection being either the maximum possible or one smaller. We unify and extend numerous previous results in a common framework, recognizing that a particular subgroup reveals important structural information about the packing. Identifying this subgroup allows us to formulate a recursive lifting construction of packings in abelian groups of increasing exponent, as well as a product construction yielding packings in the direct product of the starting groups. We also study packings of certain negative Latin square type partial difference sets of maximum possible size in abelian groups, all but one of which have identical parameters, and show how to produce such collections using packings of Latin square type partial difference sets.
