In this paper we remove the solid incidence assumption in the characterization of J. Schillewaert (A characterization of quadrics by intersection numbers, Des. Codes Cryptogr., 47 (2008), 165–175) by proving that quadric plane incidence numbers imply quadric solid incidence numbers, except for the dual complete 11-cap of PG (4, 3). Furthermore, new characterizations of the parabolic quadric Q (4, q ) and the ovoidal cone of PG (4, q ) are provided.

中文翻译：

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PG(r, q)中$$[1,q+1,2q+1,q^2+q+1]_2$$类的分类集合，$$r\ge 3$$

在本文中，我们通过证明二次曲面关联数意味着二次曲面，在 J. Schillewaert 的表征中移除了实体关联假设（A characteristic of quadrics by intersection numbers, Des. Codes Cryptogr., 47 (2008), 165–175）发病率，除了 PG 的双重完整 11 帽 (4, 3)。此外，还提供了抛物线二次曲面 Q (4, q ) 和 PG (4, q ) 的卵形圆锥的新特征。