论文标题
广义的完美差异及其应用于可变重量几何正交代码
Generalized perfect difference families and their application to variable-weight geometric orthogonal codes
论文作者
论文摘要
Wang等人在几何正交代码（GOC）中的应用。介绍了广义完美差异系列（PDF）的概念，并建立了GOCS与某种类型的广义PDF之间的等效性。基于关系，我们在本文中讨论了广义$（N \ Times M，K，1）$ -PDF的存在问题。通过使用一些辅助设计，例如半完美组可分割的设计和几种递归构造，我们证明存在概括（n \ times m，\ {3,4 \}，1）$ - pdf时，仅当$ nm \ equiv1 \ equiv1 \ pmod pmod {6} $时才存在。除了几个值外，也可能完全解决了广义$（n \ times m，\ {3,4,5 \}，1）$ -PDF的存在。结果，获得了一些可变重量完美$（N \ times m，k，1）$ - gocs。\ vspace {0.2cm} {\ bf关键字}：广义的完美差异家庭，广义的完美差异包装，几何正交代码，半完美组可分割的设计
Motivated by the application in geometric orthogonal codes (GOCs), Wang et al. introduced the concept of generalized perfect difference families (PDFs), and established the equivalence between GOCs and a certain type of generalized PDFs recently. Based on the relationship, we discuss the existence problem of generalized $(n\times m,K,1)$-PDFs in this paper. By using some auxiliary designs such as semi-perfect group divisible designs and several recursive constructions, we prove that a generalized $(n\times m, \{3,4\}, 1)$-PDF exists if and only if $nm\equiv1\pmod{6}$. The existence of a generalized $(n\times m, \{3,4,5\}, 1)$-PDF is also completely solved possibly except for a few values. As a consequence, some variable-weight perfect $(n\times m,K,1)$-GOCs are obtained.\vspace{0.2cm} {\bf Keywords}: generalized perfect difference family, generalized perfect difference packing, geometric orthogonal code, semi-perfect group divisible design
