Study on higher dimensional dual hyperovals and related functions on finite fields
| Project/Area Number |
26400029
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kagawa National College of Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 代数学 / 代数的組合せ論 / 有限幾何学 / 高次元双対超卵形 / APN関数 / 半体 / 有限射影平面 / 有限射影空間 |
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| Outline of Final Research Achievements |
We discovered a family of dual hyperovals S_c(l,GF(2r)), where l, r integers and c an element of the field GF(2r). Using these dual hyperovals S_c(l,GF(2r)), we construct many simply connected examples which are not known before. We describe the cover and quotient relations among them using elements c and the integers l and r, and determined the automorphism groups of them. Next we construct dual hyperovals using a commutative presemified and determined the isomorphism problems among them. By extending this idea, we also construct dual hyperovals using many presemifields which may not be commutative. We determined the isomorphism problems among them under the specific conditions, such as the presemifields are not isotopic to commutative presemifields. Lastly, we construct a quadratic APN function using a bent function of special type. Only two examples of such constructions were known before. It is proved that our construction are not equivalent to the former two examples.
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Report
(5 results)
Research Products
(22 results)
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[Presentation] 半体と双対超卵形2016
Author(s)
谷口浩朗
Organizer
「有限幾何とその周辺-平峰先生を偲んで」研究集会
Place of Presentation
熊本大学
Year and Date
2016-03-05
Related Report
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