2006 Fiscal Year Final Research Report Summary
Coding theory, the invariant theory for the finite fractional linear transformation groups and their applications to the number theory
| Project/Area Number |
17540006
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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, Professor, 理学部, 教授 (90087073)
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| Co-Investigator(Kenkyū-buntansha) |
BANNAI Eiichi Kyushu University, Faculty of Mathematics, Professor, 大学院数理科学研究院, 教授 (10011652)
KIZUME Masaaki Chiba University, Faculty of Science, Professor, 理学部, 教授 (60204898)
SAWADA Hideki Yamagata University, Networking and Computing Service Center, Professor, 情報基盤センター, 教授 (30095856)
MURABAYASHI Naoki Yamagata University, Faculty of Science, associate professor, 理学部, 助教授 (80261676)
NISHIMURA Takuji Yamagata University, Faculty of Science, assistant, 理学部, 助手 (90333947)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Code / multiple weight enumerator / lattice / Siegel modular form |
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| Research Abstract |
Ozeki has obtained a remarkable result concerning the 40 dimensional even unimodular lattices. The result says that there are a pair of non equivalent 40 dimensional even unimodular lattices whose Siegel theta series of degree up to 2 coincide but Siegel theta series of degree 3 differ. Ozeki has recently completed the result as a research paper under the title "On a problem posed by S. Manni". Ozeki has conceived a new approach to the problem of determining the covering radius of n dimensional lattice covering by equal spheres, and he is preparing a research paper under the title "Two approaches to the lattice covering of whole space with equal spheres in general dimensions. He is now investigating the coset weight distributions of second order Reed-Muller code of length 64.
Sawada has published two research papers including a paper entitled "On the utility of a bilateral system".
Bannai has published seven research papers including a paper entitled "A note on integral Euclidean lattices in dimension 3". Kitazume has published two research papers which discuss the relation between the finite permutation groups and the self-dual codes.
Murabayashi has published a paper entitled.
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