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The dual Yoshiara construction gives new extended generalized quadrangles
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,qβ1). He also constructed such a family S(γ) from a hyperoval γ 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 γ has o-polynomial a monomial and γ is not regular, then the dual of S(γ) is a new Yoshiara family. This article extends this result and shows that in general the dual of S(γ) is a new Yoshiara family, thus giving new extended generalized quadrangles.S. G. Barwick and Matthew R. Brownhttp://www.elsevier.com/wps/find/journaldescription.cws_home/622824/description#descriptio