Study on Insertion/Deletion by Mathematical Method of Root Systems
| Project/Area Number |
18H01435
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Review Section |
Basic Section 21020:Communication and network engineering-related
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| Research Institution | Chiba University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
仲田 研登 岡山大学, 教育学研究科, 准教授 (70532555)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000)
Fiscal Year 2020: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2018: ¥5,980,000 (Direct Cost: ¥4,600,000、Indirect Cost: ¥1,380,000)
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| Keywords | 符号理論 / 削除誤り訂正符号 / 削除 / ワイル群 / ミヌスクル表現 / 挿入 / 削除符号 / 削除誤り / ルート系 / ディンキン図 / d-完全半順序集合 / 誤り訂正符号 / リー理論 / Weyl群 / 組合せ論 / 表現論的組合せ論 / 挿入／削除符号 / ミヌスクル半順序集合 |
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| Outline of Final Research Achievements |
This research is a study of insertion/deletion focusing on mathematical objects associated with root systems. The following results are obtained: (1) Research on BAD codes," which is the motivation of this study. (2) Research on decoding algorithms for BAD codes and Levenshtein codes and (3) Construction of perfect codes corresponding to root systems including types A, B, and D. (4) Application to ordered set theory, especially d-complete ordered set, as mathematical research from root systems view points. (5) Application to quantum communication, as applications of this study.
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| Academic Significance and Societal Importance of the Research Achievements |
挿入／削除誤り訂正符号はそれ自体が符号理論の研究対象として高く注目されている。それとはまったく無縁と思われた数学対象ルート系との関連が垣間見れたことで、科学の不思議な繋がりが示唆された研究となった。符号理論としての成果だけでなく、ゲーム理論や量子計算などの成果も得られたことで、幅広い分野に影響を与える研究となった。
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Report
(4 results)
Research Products
(52 results)
