论文标题
俱乐部及其申请
Clubs and their applications
论文作者
论文摘要
排名k的俱乐部是Fancsali和Sziklai在2006年引入的有限几何形状中的良好物体。在与一种特殊类型的ARCS KM-ARCS的连接之后，它们恢复了兴趣。本文旨在研究PG $（1，Q^n）$的等级N俱乐部。我们为等级n的（n-2） - clubs提供了分类结果，我们分析了$ \ mathrm {γl}（2，q^n）$ - 定义俱乐部的已知子空间的等效性，因为其中一些问题是在确定是否等于某些散射空间时会翻译问题。然后，我们通过一些线性化的多项式发现了已知俱乐部家族的多项式描述。然后，我们将结果应用于阻塞集，KM-ARCS，多项式和等级指标的理论，从而获得了新的结构和分类结果。
Clubs of rank k are well-celebrated objects in finite geometries introduced by Fancsali and Sziklai in 2006. After the connection with a special type of arcs known as KM-arcs, they renewed their interest. This paper aims to study clubs of rank n in PG$(1,q^n)$. We provide a classification result for (n-2)-clubs of rank n, we analyze the $\mathrm{ΓL}(2,q^n)$-equivalence of the known subspaces defining clubs, for some of them the problem is then translated in determining whether or not certain scattered spaces are equivalent. Then we find a polynomial description of the known families of clubs via some linearized polynomials. Then we apply our results to the theory of blocking sets, KM-arcs, polynomials and rank metric codes, obtaining new constructions and classification results.
