| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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.
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