有限体上の符号の被覆半径と格子群の被覆半径の決定問題

确定有限域上代码覆盖半径和格群覆盖半径的问题

• 批准号: 07210209
• 负责人: 小関 道夫
• 金额: $ 0.45万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-07210209/
• 关键词: 符号の被覆半径; 符号のヤコビ多項式; アソシエーション・スキーム; 複素鏡映群

今年度の研究課題は、有限体上の符号の被覆半径と格子群の被覆半径の決定問題であった。研究代表者 小関が発案した符号のヤコビ多項式(環)の研究はこの1,2年のうちに目覚ましい進展を遂げつつある。ヤコビ多項式環は符号の同値性に対する不変量を統括することを意図して考え出された概念であるが、他の分野との関連も見いだされ始めている。それらの関連分野のうちで最もつながりが深く、また重要と思われるものとして、有限ユニタリ鏡映群の同時不変式環、ジーゲル・ヤコビ形式の理論への構成と構造の研究、アソシエーションスキーム理論、符号の被覆半径と格子群の被覆半径の決定問題等が挙げられる。符号のヤコビ多項式環の構造理論は符号の重み枚挙多項式を不変にする変換群が有限ユニタリ鏡映群のうちのいくつかの重要なものになる場合、坂内英一、坂内悦子(共に九州大)寺西鎮男(名古屋大)諸氏の共同研究の結果、基本的課題を達成し得て目下共同論文を準備中である。ジーゲル・ヤコビ形式の理論への構成と構造の研究との関連については坂内英一との共著のレジュメが学士院の紀要に出たばかりであるが、これも細部を完成して共同論文として発表する予定。符号の被覆半径の決定問題への応用についてはアイデアが簡単に証明できる定理に基づいているが、膨大な計算も必要なのでこの方面の仕事は論文を準備中の段階である。本研究と関係して主催したシンポジウム1.研究集会「代数学と計算」、東京都立大学理学部、1995 11月13日〜11月16日参加者56名

This year's research project, symbol "covering radius" and "lattice group" covering radius on a finite body determine the problem. The representative of the research group, the research representative, has studied the symbols and the multi-item formula (multi-item) for 1 year, and the progress of the project has been completed for 2 years. The symbol of the multi-project environment is the same as that of the environment. This is a comprehensive survey of the concept of environmental protection, which is based on the concept of environmental protection. The most important information, the most important, important, Symbols for the theory of multi-project environmental engineering, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, symbols for multi-project environmental engineering theory, for multi-project environmental engineering theory, for multi-project environmental engineering theory, for multi-project environmental engineering In the form of the theory, the theory was completed, the research was completed, and the academy was co-authored by Hideki Sakauchi, the academy of scholarships. The symbol "covering radius" determines the problem, and the symbol is used to determine the problem. The symbol is used to determine the problem. The symbol "covering radius" determines the problem, the symbol "covering radius" determines the problem, the symbol "covering radius" determines the problem, and the symbol "covering radius" determines the problem. In this study, the main purpose of this study is to urge the students to pay attention to their needs. Research rally "Algebra calculation", Department of Science, Beijing Capital University, 56 participants from November 13 to November 16, 1995

项目成果

N.Murabayashi: "The field of moduli of abelian surfaces with complex multiplication." To appear in J.reine angew. Math.470. (1996)

N.Murabayashi：“具有复数乘法的阿贝尔曲面的模域。”

M.Kida.: "Galois descent and twist of an abelian variety." Acta Arithmetica. 73. 51-57 (1995)

M.Kida.：“伽罗瓦血统和阿贝尔变体的扭曲。”

E,Bannai and M,Ozeki: "Coustruction of Jacobi torms from certain combinatorial polynomials" Proc. Japan Academy, Ser.A. 72. 12-15 (1996)

E，Bannai 和 M，Ozeki：“从某些组合多项式构造雅可比托”Proc。

E,Bannai S,Minashima and M,Ozeki: "On Jacobi torms of weight 4" To appear in Kyushu J, Math.(1996)

E,Bannai S,Minashima 和 M,Ozeki：“论雅可比重量 4” 出现在九州杂志，数学（1996 年）

M,Ozeki: "On the notion of Jacobi polynomials for codes" To appearin Math, Proc. Cambridge Phil, Soc.(1996)

M，Ozeki：“关于代码的雅可比多项式的概念”出现在 Math，Proc。