It is shown in Yoshiara (2004) that, if 845dff9bb032121e41e88" title="Click to view the MathML source">d-dimensional dual hyperovals exist in 9ee1747cd881f97a29f97ddfaf" title="Click to view the MathML source">V(n,2) (GF(2)-vector space of rank 8437bec" title="Click to view the MathML source">n), then 9c6b29bcaab75975a001ebfb7" title="Click to view the MathML source">2d+1≤n≤(d+1)(d+2)/2+2, and conjectured that n≤(d+1)(d+2)/2. Known bilinear dual hyperovals in 9e382e75a5e0846a6d7" 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 84dabe48e41d51234d4cb58d26"> and 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 9ed7f106d4206deb81a4274af57f214" title="Click to view the MathML source">V(2d+1,2) if 845dff9bb032121e41e88" 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 9ed7f106d4206deb81a4274af57f214" title="Click to view the MathML source">V(2d+1,2). We also determine the automorphism group of Sc(l,GF(2r)), and show that Aut(Sc(l2,GF(2rl1)))<Aut(Sc(l,GF(2r))).