m-Systems and Partial m-Systemsof Polar Spaces

Authors:
E. E. Shult;J. A. Thas
Affiliations:
Kansas State University, Department of Mathematics, Cardwell Hall, Manhattan, Kansas 66506-2602, U.S.A.;University of Ghent, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281, B-9000 Gent, BELGIUM
Venue:
Designs, Codes and Cryptography - Special issue dedicated to Hanfried Lenz
Year:
1996

Citing 3
Cited 3

Designs and their codes

Designs and their codes
m-systems of polar spaces

Journal of Combinatorial Theory Series A
Some p-Ranks Related to Orthogonal Spaces

Journal of Algebraic Combinatorics: An International Journal

Complete Systems of Lines on a Hermitian Surface over aFinite Field

Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Partial and semipartial geometries: an update

Discrete Mathematics - Special issue: Combinatorics 2000
The p-Rank of the Incidence Matrix of Intersecting Linear Subspaces

Designs, Codes and Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let P be a finite classical polar spaceof rank r, with r\ge 2. A partial m-systemM of P, with 0\le m\le r-1,is any set \{ \pi_1,\pi_2,\dots,\pi_k\} of k(\neq 0) totally singular m-spacesof P such that no maximal totally singular spacecontaining \pi_i has a point in common with (\pi_1\cup\pi_2\cup\cdots \cup \pi_k)-\pi_i, i=1,2,\dots,k. In aprevious paper an upper bound \delta for |M|was obtained (Theorem 1). If |M|=\delta, then Mis called an m-system of P. For m=0the m-systems are the ovoids of P;for m=r-1 the m-systems are the spreadsof P. In this paper we improve in many cases theupper bound for the number of elements of a partial m-system,thus proving the nonexistence of several classes of m-systems.