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Coding theory, the invariant theory for the finite fractional linear transformation groups and their applications to the number theory

编码理论、有限分数线性变换群的不变理论及其在数论中的应用

基本信息

批准号：
17540006
负责人：
OZEKI Michio
金额：
$ 1.02万
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：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540006/
关键词：
Code multiple weight enumerator lattice Siegel modular form 多重重み枚挙多項式二次形式

项目摘要

Ozeki has obtained a remarkable result concerning the 40 dimensional even unimodular lattices. The result says that there are a pair of non equivalent 40 dimensional even unimodular lattices whose Siegel theta series of degree up to 2 coincide but Siegel theta series of degree 3 differ. Ozeki has recently completed the result as a research paper under the title "On a problem posed by S. Manni". Ozeki has conceived a new approach to the problem of determining the covering radius of n dimensional lattice covering by equal spheres, and he is preparing a research paper under the title "Two approaches to the lattice covering of whole space with equal spheres in general dimensions. He is now investigating the coset weight distributions of second order Reed-Muller code of length 64.Sawada has published two research papers including a paper entitled "On the utility of a bilateral system".Bannai has published seven research papers including a paper entitled "A note on integral Euclidean lattices in dimension 3". Kitazume has published two research papers which discuss the relation between the finite permutation groups and the self-dual codes.Murabayashi has published a paper entitled.

关于40维偶幺模格，Ozeki得到了一个显著的结果。结果表明，存在一对不等价的40维偶幺模格，它们的Siegel θ级数在2次以下重合，而3次的Siegel θ级数不同. Ozeki最近完成了一个研究论文，标题为“关于S。曼尼”。Ozeki设想了一种新的方法来确定由相等球体覆盖的n维格的覆盖半径的问题，他正在准备一份研究论文，标题为“两种方法来覆盖整个空间的相等球体在一般维度。他现在正在研究长度为64的二阶Reed-Muller码的陪集重量分布。Sawada发表了两篇研究论文，其中一篇题为“On the utility of a bilateral system”。Bannai发表了七篇研究论文，其中一篇题为“A note on integral Euclidean lattices in dimension 3”。Kitazzawa发表了两篇研究论文，讨论了有限置换群与自对偶码之间的关系。