论文标题
线性和圆形的单更改涵盖设计已重新访问
Linear and Circular Single Change Covering Designs Re-visited
论文作者
论文摘要
a \ textbf {单个更改覆盖设计}是$ v $ -set $ x $和有订购的列表$ \ cl $ $ b $ b $ size $ k $的块，其中每个$ t $ set必须在至少一个块中发生。每对连续块恰好差异一个元素。当第一个和最后一个块也不同于一个元素时，单个更改覆盖设计是圆形的。如果不能为给定的$ V，K $构建其他较小的设计，则单个更改覆盖的设计最少。 在本文中，我们使用新的递归结构来解决所有$ v $的圆形\ sccd（$ v，4，b $）的存在和三种残留类别的圆形\ sccd（$ v，5，b $）模量16。我们解决了三个残留类别的存在\ sccd $（5，v，v，v，b）$ modulo 16。 \ sccd $（2c（k-1）+1，k，c^2（2k-2）+c）$，对于所有$ c \ geq 1，k \ geq2 $，都使用差异方法。
A \textbf{single change covering design} is a $v$-set $X$ and an ordered list $\cL$ of $b$ blocks of size $k$ where every $t$-set must occur in at least one block. Each pair of consecutive blocks differs by exactly one element. A single change covering design is circular when the first and last blocks also differ by one element. A single change covering design is minimum if no other smaller design can be constructed for a given $v, k$. In this paper we use a new recursive construction to solve the existence of circular \sccd($v,4,b$) for all $v$ and three residue classes of circular \sccd($v,5,b$) modulo 16. We solve the existence of three residue classes of \sccd$(v,5,b)$ modulo 16. We prove the existence of circular \sccd$(2c(k-1)+1,k,c^2(2k-2)+c)$, for all $c\geq 1, k\geq2 $, using difference methods.
