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Type: Journal article
Title: The dual Yoshiara construction gives new extended generalized quadrangles
Author: Barwick, S.
Brown, M.
Citation: European Journal of Combinatorics, 2004; 25(3):377-382
Publisher: Academic Press Ltd Elsevier Science Ltd
Issue Date: 2004
ISSN: 0195-6698
Statement of
S. G. Barwick and Matthew R. Brown
Abstract: A Yoshiara family is a set of q+3 planes in PG(5,q),q even, such that for any element of the set the intersection with the remaining q+2 elements forms a hyperoval. In 1998 Yoshiara showed that such a family gives rise to an extended generalized quadrangle of order (q+1,q−1). He also constructed such a family S(〇) from a hyperoval 〇 in PG(2,q). In 2000 Ng and Wild showed that the dual of a Yoshiara family is also a Yoshiara family. They showed that if 〇 has o-polynomial a monomial and 〇 is not regular, then the dual of S(〇) is a new Yoshiara family. This article extends this result and shows that in general the dual of S(〇) is a new Yoshiara family, thus giving new extended generalized quadrangles.
DOI: 10.1016/j.ejc.2003.09.007
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Appears in Collections:Aurora harvest
Pure Mathematics publications

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