A study of the interacting area among the theory of quadratic forms and the theory of modular forms and the algebraic coding theory

二次型理论与模型理论及代数编码理论相互作用的研究

• 批准号: 14540004
• 负责人: OZEKI Michio
• 金额: $ 2.56万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540004/
• 关键词: Coding theory; lattice; Jacobi form; Siegel modular forms; 保型形式

The present research has been done in the period between year 2002 and 2004 under the GRANT-IN-AID sponcered by the Ministry of Education, Culture, Sports, Science and Technology.In the application the head investigator raised five reseach purposes : (1)a study of the ineraction between the coding theory and the theory of modular forms, (2)a study of the lattices constructed from the binary self-dual code and the tertiary self dual codes, (3)the covering radius problem for the n-dimensional lattices, (4)the covering radius problem for non self-dual linear codes, (5)an interaction bewtween the coding theory and the cryptology.As to the purpose (1) we get some results and gave 4 talks and are preparing the research papers.As to (2) we have published one research paper and are preparing one paper.As to (3) the result is not mature for writing a paper.As to (4) we gave two talks and are preparing some research papers.There is no actual activity fot the purpose (5).Besides the research purpose we have published three research papers.

本研究是在2002年至2004年期间，在文部科技部资助下进行的。在应用中，首席研究员提出了五个研究目的：(1)研究编码理论与模形式理论之间的相互作用；(2)研究由二元自对偶码和三重自对偶码构成的格；(3)n维格的覆盖半径问题；(4)非自对偶线性码的覆盖半径问题，(5)编码理论与密码学的相互作用。对于目的(1)我们取得了一些成果，做了4次报告，正在准备研究论文。关于(2)我们已经发表了一篇研究论文，正在准备一篇论文。关于(3)结果还不成熟写一篇论文。关于(4)我们已经做了两次报告，正在准备一些研究论文。(5)没有实际的活动。

项目成果

Covering radius problem for singly even self-dual binary codes.

单偶自对偶二进制码的覆盖半径问题。

• 发表时间: 2002
• 期刊: IEEE Transaction on Information Theory 48
• 作者: M.Harada;M.Araya;H.Kharaghani;N.Murabayashi;T.Nishimura;M.Ozeki;M.Ozeki;M.Ozeki
• 通讯作者: M.Ozeki

On QM-abelian surfaces with model of GL_2-type over Q

在 QM-阿贝尔曲面上，Q 上具有 GL_2 型模型

• 发表时间: 2005
• 期刊: Journal of Number Theory 112
• 作者: Naoki Murabayashi

Even unimodular Gaussian lattices of rank 12

甚至 12 阶单模高斯格子

• 发表时间: 2002
• 期刊: Journal of Number Theory 95
• 作者: A.Kitazume;A.Munemasa
• 通讯作者: A.Munemasa

Tertiary code construction of odd unimodular extremal lattices

奇单模极值格的三级码构造

• 发表时间: 2002
• 期刊: Journal of Algebraic Combinatorics Vol.16
• 作者: M.Harada;M.Kitazume;M.Ozeki
• 通讯作者: M.Ozeki

M.Kitazume, M.Harada: "Z_6-Code Constructions of the Leech Lattice and the Niemeier Lattieces"European Journal of Combinatorics. 23. 573-581 (2002)

M.Kitazume、M.Harada：“Leech 格子和 Niemeier 格子的 Z_6 代码构造”欧洲组合学杂志。