arXiv math/04030312004-03-02math.CO

射影空间中与余维为2的子空间不相交的完备帽

Complete caps in projective space which are disjoint from a subspace of codimension two

David L. Wehlau

备注：: 13 pages. This is a corrected version of a paper that appeared in Finite Geometries, A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas, Editors, Kluwer Academic Publishing, Dordrecht, 2001, 347--361. The proof of Theorem 4.1 has been corrected as have the statements of Propositions 7.1 and 8.1

摘要：

在二阶域上，我们考虑了与射影空间的某个余维为2的子空间不相交的完备帽（不含三个共线点的极大点集）。我们推导出这样的上限必须满足的限制性条件，以便是完整的。利用这些条件，我们得到明确的描述，完全帽不满足每个超平面在至少5个点。特别是，我们确定了所有这些完整的上限在所有维度的基数集。

英文摘要：

Working over the field of order 2 we consider those complete caps (maximal sets of points with no three collinear) which are disjoint from some codimension 2 subspace of projective space. We derive restrictive conditions which such a cap must satisfy in order to be complete. Using these conditions we obtain explicit descriptions of complete caps which do not meet every hyperplane in at least 5 points. In particular, we determine the set of cardinalities of all such complete caps in all dimensions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文

AG（4，3）的最大上限划分

${\rm PG}(4n + 1, q)$中的小型完整帽

射影空间中半径$R$、余维数$tR$和$tR+\frac{R}{2}$及饱和集的新覆盖码