Dimensional dual hyperovals and APN functions with translation groups
Dimensional dual hyperovals and APN functions with translation groups
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DOI：
10.1007/s10801-013-0454-9
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发表时间：
2014-03
影响因子：
0.8
通讯作者：
U. Dempwolff;Yves Edel
中科院分区：
文献类型：
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作者：
U. Dempwolff;Yves Edel
本文建立了一维对偶超椭圆和APN函数的平移群理论。可以看出，这两种理论在很大程度上是可以同时处理的。对于小的环境空间，将证明平移群在各自几何对象的自同构群中是正规的。对于较大的环境空间，可能有多个翻译组。我们将确定自同构群中翻译群的正常闭包结构，我们将展示实际上允许多个翻译群的例子。
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.