Study on Insertion/Deletion by Mathematical Method of Root Systems

2021 Fiscal Year Final Research Report

• Project/Area Number: 18H01435
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 21020:Communication and network engineering-related
• Research Institution: Chiba University
• Principal Investigator: Hagiwara Manabu 千葉大学, 大学院理学研究院, 教授 (80415728)
• Co-Investigator(Kenkyū-buntansha): 仲田 研登 岡山大学, 教育学研究科, 准教授 (70532555)
• Project Period (FY): 2018-04-01 – 2021-03-31
• 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

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.

Free Research Field

符号理論

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。