2016 Fiscal Year Final Research Report
Research on algebraic curves in coding theory
| Project/Area Number |
25800090
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Shiga University of Medical Science |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Keywords | 代数曲線 / 符号理論 / 有理点 |
|---|
| Outline of Final Research Achievements |
In 1970's Goppa discovered algebro-geometric codes, where we need explicit curves with many rational points to construct good codes. A curve attaining the Hasse-Weil bound is called a maximal curve, and there are many interesting research on it. However we do not know the property of a curve attaining Serre's bound which is not maximal. Recently we found that the sextics, defined by Wiman in 1895 and by Edge in 1980, attain the Hasse-Weil-Serre bound over some finite fields. For some sextics among them, we determined the precise condition on the finite field over which the sextics attain the Hasse-Weil-Serre bound.
|
| Free Research Field |
代数幾何符号
|
