Study on complex spherical codes and designs
| Project/Area Number |
18K03395
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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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| Review Section |
Basic Section 12030:Basic mathematics-related
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| Research Institution | 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群) (2019-2022)
Aichi University of Education (2018) |
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Principal Investigator |
Suda Sho 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群), 総合教育学群, 准教授 (30710206)
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| Co-Investigator(Kenkyū-buntansha) |
谷口 哲至 広島工業大学, 工学部, 准教授 (90543728)
Gavrilyuk Alexander 島根大学, 学術研究院理工学系, 講師 (20897946)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 可換アソシエーション・スキーム / 符号 / デザイン / エルミート隣接行列 / 不定値内積空間 / 半正定値計画法 / アダマール行列 / 有限射影平面 / アソシエーションスキーム / optilmal code / weighing matrix / balanced weighing matrix / 数独 / 直交数独 / 強正則グラフ / Q-多項式コヒアラント配置 / Divisible design digraph / Orthogonla design / Equiangular tight frame / BGW / Hermite adjacency matrix / 不定値ユニタリ群 / directed Deza graph / disjoint weighing matrix / 直交配列 / 等角直線族 / 不変なアダマール行列 / MUB / SIC-POVM |
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| Outline of Final Research Achievements |
I conducted research on code and design on the complex sphere. As a significant contribution, I established the framework of semidefinite programming on the complex sphere and developed the theory of codes with indefinite inner products on the complex sphere. These achievements hold the potential for further advancement in code theory on the complex sphere, which was previously based on linear programming. Additionally, the application of code theory on the complex sphere with indefinite inner products, which was not initially anticipated at the start of the research, shows promise in the context of the eigenvalue multiplicities of Hermitian adjacency matrices of directed graphs, suggesting future developments.
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| Academic Significance and Societal Importance of the Research Achievements |
複素球面上の符号・デザインの進展は、代数的組合せ論の重要な研究対象である可換アソシエーション・スキームと密接に関連する研究である。さらに複素MUBやSICPOVM、equiangular tight frameといった対象への応用が見込まれる。さらに不定値内積空間の符号理論の進展は、そのエルミート隣接行列の固有値を介して、有向グラフへの応用が見込まれる。研究成果の学術的意義は高いといえる。
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Report
(6 results)
Research Products
(43 results)
