Isomorphisms between Subiaco \(q\)-clan geometries (Q1890772)

This is an investigation of the generalized quadrangle associated to the Subiaco (hyper)oval in a finite projective plane of order \(q = 2^h\), following two other papers by \textit{L. Bader, G. Lunardon} and the first author [same journal 1, No. 3, 301-328 (1994; Zbl 0803.51006)] and the first author [same journal 1, No. 3, 427-438 (1994; Zbl 0803.51007)]. It is of great interest that these structures exist for \(h\) both odd and even. In fact, a \(q\)-clan is a set of matrices from which both the oval and the quadrangle can be constructed. The authors give a canonical construction of these matrices for the Subiaco case.