Some \(p\)-ranks related to Hermitian varieties
type: Item
instance of: scholarly article
title: Some \(p\)-ranks related to Hermitian varieties
zbMATH Open document ID: 0888.51007
DOI: 10.1016/S0378-3758(96)00020-1
published in: Journal of Statistical Planning and Inference
publication date: 1997-09-09T00:00:00Z
review text: Let \(\mathcal S\) be the incidence structure consisting of the points of a nondegenerate Hermitian variety of \(PG(n,q ^2)\) and of all hyperplanes of \(PG(n,q ^2)\), where \(q = p ^e\) and \(p\) is prime. The author shows that the \(p\)-rank of any incidence matrix of \(\mathcal S\) equals \(\left[{p + n -1 \choose n}^2 - {p + n -2 \choose n}^2 \right]^e + 1\). As a corollary, he obtains some new bounds for the size of caps and the existence of ovoids in finite unitary polar spaces.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1040447
zbMATH Keywords: Hermitian variety
zbMATH Keywords: \(p\)-rank
zbMATH Keywords: incidence matrix
zbMATH Keywords: size of caps
zbMATH Keywords: existence of ovoids
zbMATH Keywords: polar spaces
author: G. Eric Moorhouse
reviewed by: Norbert Knarr
MaRDI profile type: Publication
cites work: Q4004114
cites work: Some \(p\)-ranks related to orthogonal spaces
cites work: Q4764144
cites work: On a class of majority-logic decodable cyclic codes
cites work: Q4003762
cites work: On the p-rank of the design matrix of a difference set
cites work: Q3344217
cites work: On the p-rank of the incidence matrix of points and hyperplanes in a finite projective geometry
cites work: Ovoids and spreads of finite classical polar spaces
cites work: Semi-partial geometries and spreads of classical polar spaces
full work available at URL: s0378-3758(96)00020-1
OpenAlex ID: W2147540017
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description: scientific article; zbMATH DE number 1040447