论文标题
部分可观测时空混沌系统的无模型预测
Cones from maximum $h$-scattered linear sets and a stability result
论文作者
论文摘要
本文主要关注的是最大$ h $ scaters线性集的锥体。我们首先研究此类锥体与超平面的交叉大小。然后，我们分析了两个与超平面相交大小的点集的构造。特别是，第二个扩展了在投影空间中翻译km-arcs的构建，作为无限锥的一部分，最大$ h $ scater的线性套件。作为第二构建的一个实例，我们获得了具有高卵形的圆柱体，我们称之为高赖因固定器，我们可以为此提供稳定性的结果。这些问题的主要动机与锤子和等级距离代码的连接有关。实际上，我们能够构造数量很少的代码，并为与高型固定器相关的代码提供稳定性结果。
This paper mainly focuses on cones whose basis is a maximum $h$-scattered linear set. We start by investigating the intersection sizes of such cones with the hyperplanes. Then we analyze two constructions of point sets with few intersection sizes with the hyperplanes. In particular, the second one extends the construction of translation KM-arcs in projective spaces, having as part at infinity a cone with basis a maximum $h$-scattered linear set. As an instance of the second construction we obtain cylinders with a hyperoval as basis, which we call hypercylinders, for which we are able to provide a stability result. The main motivation for these problems is related to the connections with both Hamming and rank distance codes. Indeed, we are able to construct codes with few weights and to provide a stability result for the codes associated with hypercylinders.
