A new construction of the d-dimensional Buratti-Del Fra dual hyperoval
A new construction of the d-dimensional Buratti-Del Fra dual hyperoval
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d维Buratti-Del Fra双超椭圆的新构造
DOI：
10.1016/j.ejc.2012.01.002
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发表时间：
2012
影响因子：
1
通讯作者：
H.Taniguchi and S.Yoshiara
中科院分区：
文献类型：
--
作者：
Yasuo Ohno;Jun-ichi Okuda and Wadim Zudilin;増岡 彰;Hiroaki Taniguchi and Satoshi Yoshiara;Chika Yamazaki and Yasuo Ohno;Akira Masuoka;谷口浩朗;大野泰生;増岡彰;H.Taniguchi and S.Yoshiara
Buratti - Del Fra对偶超卵圆Dd（F2）是已知的四个具有向量维数（d+1）(d+2)/2环境空间的二维单连通超卵圆无限族之一（Buratti and Del Fra(2003)[1]）。根据加法公式给出了F2上的d维对偶超卵圆被Dd（F2）覆盖的判据（命题1）。使用它，我们提供了一个更简单的Dd（F2）模型（命题3）。我们也给出了K⊕K的（d+1）维子空间的集合S[B]是Dd（F2）的商的条件（引理4），该集合由[公式：见文本]上的对称双线性形式B构造而成。当d为偶数时，给出满足这些条件的显式B。我们也证明了Dd（F2）的仿射展开被半正方体覆盖（命题10）。
The Buratti–Del Fra dual hyperoval Dd(F2) is one of the four known infinite families of simply connected d-dimensional dual hyperovals over F2with ambient space of vector dimension (d+1)(d+2)/2 (Buratti and Del Fra (2003) [1]). A criterion (Proposition 1) is given for a d-dimensional dual hyperoval over F2to be covered by Dd(F2) in terms of the addition formula. Using it, we provide a simpler model of Dd(F2) (Proposition 3). We also give conditions (Lemma 4) for a collection S[B] of (d+1)-dimensional subspaces of K⊕K constructed from a symmetric bilinear form B on [Formula: see text] to be a quotient of Dd(F2). For when d is even, an explicit form B satisfying these conditions is given. We also provide a proof for the fact that the affine expansion of Dd(F2) is covered by the halved hypercube (Proposition 10).