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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A.M.W. Hui acknowledges the support of National Natural Science Foundation of China (Grant No. 12071041).
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Barwick, S.G., Hui, A.M.W. & Jackson, WA. A geometric description of the Figueroa plane. Des. Codes Cryptogr. 91, 1581–1593 (2023). https://doi.org/10.1007/s10623-022-01158-5
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DOI: https://doi.org/10.1007/s10623-022-01158-5