A New Family of Extended Generalized Quadrangles of Order (q + 1,q − 1)

In this paper we show that any dual of the family S of planes defined by Yoshiara also satisfies the same conditions. We present a new family Y′(O) of extended generalized quadrangles of order (q + 1, q − 1) constructed from the dual of the Yoshiara construction S(O) and show that each such extended generalized quadrangle is an extension of the dual of the Tits quadrangle T2 * (O), where O is a hyperoval whose o-polynomial is a monomial.