Geodesic
Dimensional dual hyperovals and APN functions with translation groups
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 2, pp. 457-496.

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In this paper we develop a theory of translation groups for dimensional dual hyperovals and APN functions. It will be seen that both theories can be treated, to a large degree, simultaneously. For small ambient spaces it will be shown that the translation groups are normal in the automorphism group of the respective geometric object. For large ambient spaces there may be more than one translation group. We will determine the structure of the normal closure of the translation groups in the automorphism group and we will exhibit examples which in fact do admit more than one translation group.
Classification : 05B25
Keywords: dimensional dual hyperovals, APN functions, translation group, structure of automorphism group and its action, equivalence 
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     author = {Dempwolff, Ulrich and Edel, Yves},
     title = {Dimensional dual hyperovals and {APN} functions with translation groups},
     journal = {Journal of Algebraic Combinatorics},
     pages = {457--496},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2014__39_2_a1/}
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Dempwolff, Ulrich; Edel, Yves. Dimensional dual hyperovals and APN functions with translation groups. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 2, pp. 457-496. http://geodesic.mathdoc.fr/item/JAC_2014__39_2_a1/