2013 Fiscal Year Final Research Report
Study on functions on finite fields and finite geometry
| Project/Area Number |
23540037
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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) |
2011 – 2013
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| Keywords | 代数的組合せ論 / 双対超卵形 / 有限幾何学 / APN関数 |
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| Research Abstract |
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.
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