论文标题
GF（Q）的新矩形和设计的结构
Constructions of new matroids and designs over GF(q)
论文作者
论文摘要
完美的矩阵设计（PMD）是一种矩形，其等级的平坦都具有相同的尺寸。在本文中，我们介绍了PMD及其属性的Q-Analogue。为了这样做，我们首先为Q-Matroids建立了一个新的隐态定义。我们表明Q-Steiner系统是Q-PMD的示例，我们使用这种Q-ratroid结构来构建Q-Steiner Systems的子空间设计。我们将此结构应用于唯一已知的Q-Steiner系统，该系统具有参数s（2,3,13; 2），因此建立了具有参数2-（13,4,5115; 2）的新的子空间设计的存在。
A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the q-analogue of a PMD and its properties. In order to do so, we first establish a new cryptomorphic definition for q-matroids. We show that q-Steiner systems are examples of q-PMD's and we use this q-matroid structure to construct subspace designs from q-Steiner systems. We apply this construction to the only known q-Steiner system, which has parameters S(2,3,13;2), and hence establish the existence of a new subspace design with parameters 2-(13,4,5115;2).
