2004 Fiscal Year Final Research Report Summary
A study of the interacting area among the theory of quadratic forms and the theory of modular forms and the algebraic coding theory
| Project/Area Number |
14540004
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Yamagata University |
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Principal Investigator |
OZEKI Michio Yamagata University, Faculty of Science, Department of Mathematical Sciences, Professor, 理学部, 教授 (90087073)
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| Co-Investigator(Kenkyū-buntansha) |
KITAZUME Masaaki Chiba University, Faculty of Science, Professor, 理学部, 教授 (60204898)
MUNEMASA Akihiro Tohoku University, Graduate School of Information Science, Professor, 大学院・情報科学研究科, 教授 (50219862)
HARADA Masaaki Yamagata University, Faculty of Science, Department of Mathematical Sciences, Associate Professor, 理学部, 助教授 (90292408)
SAWADA Hideki Yamagata University, Networking and Computing Service Center, Professor, 学術情報基盤センター, 教授 (30095856)
MURABAYASHI Naoki Yamagata University, Faculty of Science, Department of Mathematical Sciences, Associate Professor, 理学部, 助教授 (80261676)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Coding theory / lattice / Jacobi form / Siegel modular forms |
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| Research Abstract |
The present research has been done in the period between year 2002 and 2004 under the GRANT-IN-AID sponcered by the Ministry of Education, Culture, Sports, Science and Technology.
In the application the head investigator raised five reseach purposes : (1)a study of the ineraction between the coding theory and the theory of modular forms, (2)a study of the lattices constructed from the binary self-dual code and the tertiary self dual codes, (3)the covering radius problem for the n-dimensional lattices, (4)the covering radius problem for non self-dual linear codes, (5)an interaction bewtween the coding theory and the cryptology.
As to the purpose (1) we get some results and gave 4 talks and are preparing the research papers.
As to (2) we have published one research paper and are preparing one paper.
As to (3) the result is not mature for writing a paper.
As to (4) we gave two talks and are preparing some research papers.
There is no actual activity fot the purpose (5).
Besides the research purpose we have published three research papers.
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