Some p-Ranks Related to Orthogonal Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Some p-Ranks Related to Orthogonal Spaces

Authors:	Aart Blokhuis G. Eric Moorhouse

Affiliation:	(1) Dept. of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands;(2) Dept. of Mathematics, University of Wyoming, Laramie, WY, 82071

Abstract:	We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p^e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in $O_{10}^ + (2^e ),O_{10}^ + (3^e ),O_9 (5^e ),O_{12}^ + (5^e )$ and $O_{12}^ + (7^e )$ . We also give slightly weaker bounds for more general finite classical polar spaces. Another application is the determination of certain explicit bases for the code of PG(2, p) using secants, or tangents and passants, of a nondegenerate conic.

Keywords:	p-rank quadric ovoid code
本文献已被 SpringerLink 等数据库收录！