Hokkaido Mathematical Journal

A characterization of 42 ovoids with a certain property in PG(3,2)

Koichi INOUE

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Abstract

In this paper, we characterize 42 ovoids with a certain property in a projective space PG(3,2) described in Yucas [6]. As a corollary, we construct the Steiner 4-wise balanced design S(4,{5,6},17) with 252 blocks which is an extension of the point-plane design A of an affine space AG(4,2). The construction leads to not only the uniqueness of such an extension, but also a (usual) extension of the 2-repeated design 2.A.

Article information

Source
Hokkaido Math. J., Volume 40, Number 3 (2011), 431-447.

Dates
First available in Project Euclid: 26 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1319595865

Digital Object Identifier
doi:10.14492/hokmj/1319595865

Mathematical Reviews number (MathSciNet)
MR2883500

Zentralblatt MATH identifier
1233.51002

Subjects
Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 05B25: Finite geometries [See also 51D20, 51Exx]

Keywords
Steiner 4-wise balanced design affine space orthogonal group exterior algebra alternating forms quadratic forms

Citation

INOUE, Koichi. A characterization of 42 ovoids with a certain property in PG (3,2). Hokkaido Math. J. 40 (2011), no. 3, 431--447. doi:10.14492/hokmj/1319595865. https://projecteuclid.org/euclid.hokmj/1319595865


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