具有极大非冗余覆盖和极小阻塞集的群
Groups with maximal irredundant covers and minimal blocking sets
摘要：
令$n$为正整数。用$\mathrm{PG}(n,q)$表示$q$阶有限域$\mathbb{F}_q$上的$n$维射影空间. $\mathrm{PG}(n,q)$中的阻塞集是与$\mathrm{PG}(n,q)$的每个超平面具有非空交集的点的集合。一个阻塞集称为极小的，如果它的真子集都不是阻塞集。本文证明了如果$\mathrm{PG}(n_i,q)$包含$i\in\{1,2\}$的大小为$k_i$的最小阻塞集，则$\mathrm{PG}(n_1+n_2+1,q)$包含大小为$k_1+k_2-1$的最小阻塞集.这一结果是证明了一个结果的群体与最大的非冗余覆盖。
英文摘要：
Let $n$ be a positive integer. Denote by $\mathrm{PG}(n,q)$ the $n$-dimensional projective space over the finite field $\mathbb{F}_q$ of order $q$. A blocking set in $\mathrm{PG}(n,q)$ is a set of points that has non-empty intersection with every hyperplane of $\mathrm{PG}(n,q)$. A blocking set is called minimal if none of its proper subsets are blocking sets. In this note we prove that if $\mathrm{PG}(n_i,q)$ contains a minimal blocking set of size $k_i$ for $i\in\{1,2\}$, then $\mathrm{PG}(n_1+n_2+1,q)$ contains a minimal blocking set of size $k_1+k_2-1$. This result is proved by a result on groups with maximal irredundant covers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
