2017 Fiscal Year Final Research Report
Projective geometry over finite fields and its applications to coding theory
| Project/Area Number |
15K04829
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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 | Kanagawa University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 有限体 / 射影空間 / 超曲面 |
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| Outline of Final Research Achievements |
This research project focused on the number of points of a hyper-surface in a certain projective space over a finite field.
In the previous project, we had shown, so-called, an `elementary bound' for hyper-surfaces of a fixed degree over a finite field in projective n-space, which is an upper bound of the number of rational points of hyper-surfaces without linear components, and, for n = 3, we had determined the all optimal surfaces in the sense of this bound.
In this project, we handled hyper-surfaces without singular points. For odd number n, we got an upper bound for the number of points of those hyper-surfaces, and settled the problem of finding all optimal hyper-surfaces in the sense of this bound.
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| Free Research Field |
代数幾何
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