The automorphism groups of doubly transitive bilinear dual hyperovals
A dual hyperoval over the field \({\mathbb F}_2\) of rank \(n\) is a set \(D\) of \(2^n-1\) subspaces of some vector space \({\mathbb F}_2^m\) such that \(\dim(X\cap Y) =1\) and \(\dim(X\cap Y\cap Z) =0\) for any three distinct elements \(X,Y, Z \in D\). The author shows that the examples constructed by him in [Eur. J. Comb. 44, Part A, 1--22 (2015; Zbl 1341.51008)], Example 3.3, have the automorphism group \(\mathrm{A\Gamma L}(1,2^n)\). Moreover, he characterizes the \(2\)-transitive quotients of the examples of \textit{C. Huybrechts} [Discrete Math. 255, No. 1--3, 193--223 (2002; Zbl 1024.51010)] and determines their automorphism groups; the number of such quotients grows exponentially with \(n\).
scientific article; zbMATH DE number 6854787
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