Study on functions on finite fields and finite geometry

有限域函数和有限几何研究

• 批准号: 23540037
• 负责人: TANIGUCHI Hiroaki
• 金额: $ 1.41万
• 依托单位: Kagawa National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540037/
• 关键词: 代数的組合せ論; 双対超卵形; 有限幾何学; APN関数

We mainly study on APN DHO(constructed from APN functions) and bilinear DHO. We give a necessary and sufficient condition for a bilinear DHO to be an APN DHO. Using this result, we show that the dual and the transpose of the dual of the DHOs from some APN function are not known (by that time). We also give a new construction of the Buratti-Del Fra DHO. Using this construction, we show that the Buratti-Del Fra DHO is a bilinear DHO, and that the universal cover of the Buratti-Del Fra DHO is same as that of the Huybrechts DHO (APN DHO). We also give an example of a quotient of the Buratti-Del Fra DHO in PG(2d+1,2). Next, we give an uniform description for four known (all known) d-dimensional DHOs in PG(d(d+3)/2,2)(classical DHOs). We give some examples of simply connected d-dimensional DHOs in PG(n,2) with n>2d+1. Moreover, we construct many new symmetric bilinear DHOs in PG(n,2) for 2d+1<n<d(d+3)/2.

我们主要研究了由APN函数构造的APN - DHO和双线性DHO。给出了双线性DHO是APN DHO的充分必要条件。利用这一结果，我们证明了某些APN函数的dho的对偶和对偶的转置是未知的（到那时）。我们也给了一个新的建设Buratti-Del Fra DHO。利用这一构造，我们证明了Buratti-Del Fra DHO是双线性DHO，并且Buratti-Del Fra DHO的普遍覆盖范围与Huybrechts DHO （APN DHO）相同。我们还给出了PG（2d+1,2）中Buratti-Del Fra DHO的商的一个例子。接下来，我们给出了PG(d(d+3)/2,2)（经典DHOs）中四个已知的（全部已知的）d维DHOs的统一描述。我们给出了PG（n,2）中n>2d+1的单连通d维dho的一些例子。此外，我们构造了2d+1<n<d(d+3)/2的PG（n,2）中许多新的对称双线性DHOs。

项目成果

A new construction of the d-dimensional Buratti-Del Fra dual hyperoval

d维Buratti-Del Fra双超椭圆的新构造

• DOI: 10.1016/j.ejc.2012.01.002
• 发表时间: 2012
• 期刊: European Journal of Combinatorics
• 影响因子: 1
• 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
• 通讯作者: H.Taniguchi and S.Yoshiara

Bilinear dual hyperovalについて

关于双线性对偶超椭圆

• 发表时间: 2014
• 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;増岡彰;大野泰生;Hiroaki Taniguchi and Satoshi Yoshiara;大野泰生;増岡彰;Hiroaki Taniguchi;大野泰生;Hiroaki Taniguchi;Yasuo Ohno;谷口浩朗;Yasuo Ohno;谷口浩朗
• 通讯作者: 谷口浩朗

Buratti-Del Fra型のDHOについて

关于 Buratti-Del Fra 型 DHO

• 发表时间: 2013
• 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;増岡彰;大野泰生;Hiroaki Taniguchi and Satoshi Yoshiara;大野泰生;増岡彰;Hiroaki Taniguchi;大野泰生;Hiroaki Taniguchi;Yasuo Ohno;谷口浩朗;Yasuo Ohno;谷口浩朗;大野泰生;谷口浩朗
• 通讯作者: 谷口浩朗

On the dual of the dual hyperoval from APN function $f(x)=x^3+Tr(x^9)$,

在 APN 函数 $f(x)=x^3 Tr(x^9)$ 的对偶超椭圆的对偶上，

• DOI: 10.1016/j.ffa.2011.07.009
• 发表时间: 2012
• 期刊: Finite Fields and Their Applications
• 影响因子: 1
• 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;増岡彰;大野泰生;Hiroaki Taniguchi and Satoshi Yoshiara;大野泰生;増岡彰;Hiroaki Taniguchi;大野泰生;Hiroaki Taniguchi
• 通讯作者: Hiroaki Taniguchi

ある対称 双線形高次元双対超卵形の性質

某种对称双线性高维双超卵形体的性质

• 发表时间: 2013
• 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;増岡彰;大野泰生;Hiroaki Taniguchi and Satoshi Yoshiara;大野泰生;増岡彰;Hiroaki Taniguchi;大野泰生;Hiroaki Taniguchi;Yasuo Ohno;谷口浩朗;Yasuo Ohno;谷口浩朗;大野泰生;谷口浩朗;大野泰生;谷口浩朗;大野泰生;谷口浩朗;大野泰生;Hiroaki Taniguchi;On the enumeration of certain edge-colored graphs;谷口浩朗
• 通讯作者: 谷口浩朗