有限向量空间中具有高error correction度的池化设计
Pooling designs with surprisingly high degree of error correction in a finite vector space
摘要：
池化设计是许多生物技术应用中的标准实验工具。众所周知，所有著名的池化设计都是通过“包容矩阵”方法从数学结构构造的。特别是，Macula的设计（分别为Ngo和Du的设计）是由子集（分别为）的包含关系构造的。子空间）在有限集中（分别向量空间）。最近，我们推广了Macula设计，得到了一类由有限集中的子集具有更高纠错度的池化设计。在本文中，作为Ngo和Du的设计的推广，我们研究了有限向量空间中的相应问题，得到了一族具有令人惊讶的高纠错度的池化设计。我们的设计与Ngo和Du的设计分别具有相同的项目数和池数，但当空间维数足够大时，其容错性能要比D'yachkov等人在\cite{DF}中给出的Ngo和Du的设计好得多.
英文摘要：
Pooling designs are standard experimental tools in many biotechnical applications. It is well-known that all famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In particular, Macula's designs (resp. Ngo and Du's designs) are constructed by the containment relation of subsets (resp. subspaces) in a finite set (resp. vector space). Recently, we generalized Macula's designs and obtained a family of pooling designs with more high degree of error correction by subsets in a finite set. In this paper, as a generalization of Ngo and Du's designs, we study the corresponding problems in a finite vector space and obtain a family of pooling designs with surprisingly high degree of error correction. Our designs and Ngo and Du's designs have the same number of items and pools, respectively, but the error-tolerant property is much better than that of Ngo and Du's designs, which was given by D'yachkov et al. \cite{DF}, when the dimension of the space is large enough.
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