A note on relative hemisystems of Hermitian generalised quadrangles

John Bamberg; Melissa Lee; E. Swartz

doi:10.1007/s10623-015-0135-x

A note on relative hemisystems of Hermitian generalised quadrangles

John Bamberg, Melissa Lee, E. Swartz

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

© 2015, Springer Science+Business Media New York.In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q2) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.

Original language	English
Pages (from-to)	131-144
Number of pages	14
Journal	Designs, Codes, and Cryptography
Volume	81
Issue number	1
DOIs	https://doi.org/10.1007/s10623-015-0135-x
Publication status	Published - 1 Oct 2016

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10.1007/s10623-015-0135-x

https://arxiv.org/abs/1504.03435

Cayley Graphs & their Associated Geometric & Combinatorial Objects
Li, C. & Bamberg, J.
Australian Research Council
1/01/12 → 30/06/17
Project: Research
Finite geometry from an algebraic point of view
Bamberg, J.
Australian Research Council
1/01/12 → 30/06/17
Project: Research

Cite this

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title = "A note on relative hemisystems of Hermitian generalised quadrangles",

abstract = "{\textcopyright} 2015, Springer Science+Business Media New York.In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q2) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente{\textquoteright}s, and develop techniques that are likely to be useful in finding relative hemisystems in future.",

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AB - © 2015, Springer Science+Business Media New York.In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q2) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.

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A note on relative hemisystems of Hermitian generalised quadrangles

Abstract

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Projects

Cayley Graphs & their Associated Geometric & Combinatorial Objects

Finite geometry from an algebraic point of view

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