2016 Fiscal Year Final Research Report
Existence and constructions of a complete system of mutually orthogonal partial t-designs over complex fields and its application
| Project/Area Number |
26610036
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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 | Chubu University (2015-2016)
Nagoya University (2014) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 組合せデザイン / t-MOD / t-SEED / 量子ジャンプ符号 |
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| Outline of Final Research Achievements |
In this project, we introduced a notion of t-MOD, which is a mathematical formulation of a quantum jump code related to the error correction of memories of a quantum computer. A complete t-MOD with maximum dimension among t-MODs with given length and error correcting ability is considered and its combinatorial structure is characterized. We gave some nonexistence results of complete t-MOD and a example of a complete 1-MOD.
On the other hand, we obtain constructions of a binary t-MOD, called a t-SEED, by utilizing affine geometry. Moreover, we find a sufficient condition by introducing the notion of`lcm-closure' to the multifold factorization problem of cyclic groups, which is closely related to the construction of 2-SEEDs.
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| Free Research Field |
数学基礎・応用数学
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