It is shown in Yoshiara (2004) that, if ae4845dff9bb032121e41e88" title="Click to view the MathML source">d-dimensional dual hyperovals exist in 9779ee1747cd881f97a29f97ddfaf" title="Click to view the MathML source">V(n,2) (8bafb619f37e4e3d0f3" title="Click to view the MathML source">GF(2)-vector space of rank e52ed78437bec" title="Click to view the MathML source">n), then 975a001ebfb7" title="Click to view the MathML source">2d+1≤n≤(d+1)(d+2)/2+2, and conjectured that ae76d592c14d3110c907f389a8ab28f" title="Click to view the MathML source">n≤(d+1)(d+2)/2. Known bilinear dual hyperovals in 8b3bc049e382e75a5e0846a6d7" title="Click to view the MathML source">V((d+1)(d+2)/2,2) are the Huybrechts dual hyperoval and the Buratti–Del Fra dual hyperoval. In this paper, we investigate on the covering map , where the dual hyperovals and 8c3dcb50cc3daa6b8dc1fdb3a3a7c" title="Click to view the MathML source">Sc(l,GF(2r)) are constructed in Taniguchi (2014). Using the result, we show that the Buratti–Del Fra dual hyperoval has a bilinear quotient in V(2d+1,2) if ae4845dff9bb032121e41e88" title="Click to view the MathML source">d is odd. On the other hand, we show that the Huybrechts dual hyperoval has no bilinear quotient in V(2d+1,2). We also determine the automorphism group of 8c3dcb50cc3daa6b8dc1fdb3a3a7c" title="Click to view the MathML source">Sc(l,GF(2r)), and show that Aut(Sc(l2,GF(2rl1)))<Aut(Sc(l,GF(2r))).