2015 Fiscal Year Final Research Report
Research on the general theory of algebraic-geometric codes
| Project/Area Number |
24540052
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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 | Japan Women's University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 代数幾何符号 / ベクトル束 |
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| Outline of Final Research Achievements |
The technique of error-correcting codes is an indispensable tool in the modern data transmission. Among them, the algebraic-geometric codes constructed from the geometry of algebraic varieties defined over finite fields are equipped with excellent asymptotic properties. In the present research, we proposed to establish the general theory which unifies the known algebraic-geometric codes and investigated its fundamental properties. As a result of the research, we constructed some algebraic-geometric codes of novel type from vector bundles on algebraic varieties defined over function fields or arithmetic varieties and determined their parameters.
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| Free Research Field |
代数幾何学
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