Geodesic
Extensions of $\mathrm{GQ}(4,2)$, the description of hyperovals
Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 101-116.

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A subgraph of the point graph of the generalized quadrangle $\mathrm{GQ}(s,t)$ is called a hyperoval, if it is a regular graph without triangles of valence $t+1$ with even number of vertices. In the triangular extensions of $\mathrm{GQ}(s,t)$ the role of $\mu$-subgraphs can be played by hyperovals only. We give a classification of the hyperovals in $\mathrm{GQ}(4,2)$. For any even $\mu$ from 6 to 18 there exists a hyperoval with $\mu$ points. This research was supported by the Russian Foundation for Basic Research, grant 94–01–00802–a. 
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     author = {A. A. Makhnev},
     title = {Extensions of $\mathrm{GQ}(4,2)$, the description of hyperovals},
     journal = {Diskretnaya Matematika},
     pages = {101--116},
     publisher = {mathdoc},
     volume = {9},
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     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_3_a8/}
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A. A. Makhnev. Extensions of $\mathrm{GQ}(4,2)$, the description of hyperovals. Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 101-116. http://geodesic.mathdoc.fr/item/DM_1997_9_3_a8/