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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 5/2023

28-12-2022

A geometric description of the Figueroa plane

Authors: S. G. Barwick, Alice M. W. Hui, Wen-Ai Jackson

Published in: Designs, Codes and Cryptography | Issue 5/2023

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Abstract

The Figueroa planes are of particular interest as one of the few known families of non-translation projective planes. The Figueroa planes are constructed from the Desarguesian plane \({PG }(2,q^3)\) by replacing the lines of \({PG }(2,q^3)\) with a new set of lines. This article presents a new geometric construction of the Figueroa plane of order \(q^3\) for q a prime power, \(q>2\), \(q\not \equiv 1\pmod 3\). The construction uses \(\mathbb {F}_{q}\)-conics of \({PG }(2,q^3)\).
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Metadata
Title
A geometric description of the Figueroa plane
Authors
S. G. Barwick
Alice M. W. Hui
Wen-Ai Jackson
Publication date
28-12-2022
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 5/2023
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-022-01158-5

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