Quasi-quadrics and related structures
Quasi-quadrics and related structures
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发表时间：
2000
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通讯作者：
F. Clerck;Nicholas A. Hamilton;C. O'Keefe;Tim Penttila
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作者：
F. Clerck;Nicholas A. Hamilton;C. O'Keefe;Tim Penttila
在射影空间PG（n，q）中，拟二次曲面是一组点，它们与超平面的交数与该空间中非退化二次曲面的交数相同。当然，非退化二次曲面本身是拟二次曲面的例子，但许多其他例子是明确的。在n为奇数的情况下，拟二次曲面与超平面的交截有两种大小，双特征标集也是如此。这些集合被认为是强正则图、双权码、不等权集、SDP-设计、Reed-Muller码和Bent函数。当n为偶数时，拟二次曲面与超平面的交有三种大小。其中某些可用于构造完全图的对极距离正则覆盖。本文的目的是综合有关拟二次曲面的许多已知结果，并提供一些新的几何构造方法和定理。
In a projective space PG(n, q) a quasi-quadric is a set of points that has the same intersection numbers with respect to hyperplanes as a non degenerate quadric in that space. Of course, non-degenerate quadrics themselves are examples of quasi-quadrics, but many other examples ex ist. In the case that n is odd, quasi-quadrics have two sizes of inter sections with hyperplanes and so are two-character sets. These sets are known to give rise to strongly regular graphs, two-weight codes, differ ence sets, SDP-designs, Reed-Muller codes and bent functions. When n is even, quasi-quadrics have three sizes of intersection with respect to hyperplanes. Certain of these may be used to construct antipodal dis tance regular covers of complete graphs. The aim of this paper is to draw together many of the known results about quasi-quadrics, as well as to provide some new geometric construction methods and theorems.