2010 Fiscal Year Final Research Report
The study on higher dimensional dual hyperovals in finite geometry
| Project/Area Number |
20540034
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Takuma National College of Technology |
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Principal Investigator |
TANIGUCHI Hiroaki Takuma National College of Technology, 一般教育科, 教授 (60370037)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 代数的組合せ論 |
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| Research Abstract |
We study on the relation between APN (Almost Perfect Non-linear) functions, which are investigated in the field of cryptography, and dual hyperovals. Using this relation, we construct new dual hyperovals. Next, using semifields, we construct many new dual hyperovals. Moreover, we also construct many new non isomorphic quotients of the Veronesean dual hyperoval, and the Buratti Del Fra dual hyperoval in small dimensional projective spaces.
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