Challenging of the existence problem of a certain self-dual code through combinatorial designs and lattices
| Project/Area Number |
26610032
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tohoku University |
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Principal Investigator |
Harada Masaaki 東北大学, 情報科学研究科, 教授 (90292408)
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| Co-Investigator(Renkei-kenkyūsha) |
MUNEMASA Akihiro 東北大学, 大学院情報科学研究科, 教授 (50219862)
SHIMAKURA Hiroki 東北大学, 大学院情報科学研究科, 准教授 (90399791)
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 組合せ論 / 代数的符号理論 / 自己双対符号 / 格子 / 組合せデザイン |
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| Outline of Final Research Achievements |
In this project, I studied self-orthogonal designs including a self-orthogonal 5-(72,16,78) design, where the existences of such a design and an extremal doubly even self-dual code of length 72 are equivalent, with Akihiro Munemasa.
Using the classification of unimodular lattices, I gave some classification of self-dual Zk-codes. In addition, I studied supplementary difference sets related to complex spherical 2-codes.
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Report
(3 results)
Research Products
(4 results)
