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On the Constructions of Optical Orthogonal Codes from Combinatorial Design Theory

从组合设计理论探讨光学正交码的构造

基本信息

批准号：
14540100
负责人：
MIAO Ying
金额：
$ 2.24万
依托单位：
University of Tsukuba
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

项目摘要

Optical orthogonal codes are used in optical code-division multi-access communications so that multiple users can efficiently transmit and receive information in one single optic channel. It is known that an optimal optical orthogonal code is equivalent to a combinatorial structure called maximal cyclic t-difference packing. The main purpose of this research project is to construct optimal optical orthogonal codes from a combinatorial approach, that is, instead of constructing optimal optical orthogonal codes directly, we construct their corresponding maximal cyclic t-difference packings.Fuji-Hara, Miao and Mishima introduced a new concept of incomplete cyclic difference matrices, and used them to construct many cyclic t-difference packings with maximal number of blocks. Together with a computer search, many infinite families of optimal optical orthogonal codes were constructed. The existence of optimal optical orthogonal codes with weight 4, correlation constraint 1, and code length v … More with v=0 mod 24 was completely settled.Shinohara used special arcs and conies in finite geometries to construct optical orthogonal codes and obtained infinite families of asymptotic optimal optical orthogonal codes.Frequency hopping sequences are used in multi-access spread-spectrum communications which are closely related to optical orthogonal codes. Fuji-Hara, Miao and Mishima found an equivalence relationship between frequency hopping sequences and partition-type difference packings. By using this equivalence, Fuji-Hara, Miao and Mishima constructed many infinite families of optimal frequency hopping sequences.Miao also considered the security of multi-access communication systems. Topics covered include authentication codes, secret sharing schemes, ID-based signature schemes, and proxy cryptosystems.Fuji-Hara, Miao, Mishima and Shinohara also carried out theoretical research on several topics in combinatorial design theory which are related to optical orthogonal codes and frequency hopping sequences. Less

光正交码用于光码分多址通信，使得多个用户可以在单个光信道中有效地发送和接收信息。已知最优光正交码等价于称为最大循环t-差填充的组合结构。Fuji-Hara，Miao和三岛等人提出了不完全循环差矩阵的概念，并利用它构造了许多具有最大块数的循环t-差填充，而不是直接构造最优光正交码。结合计算机搜索，构造了许多最优光正交码的无限族。研究了码长为v，码重为4，相关约束为1的最优光正交码的存在性 ...更多信息 Shinohara利用有限几何中的特殊圆弧和圆锥曲线构造光正交码，得到了无限族渐近最优光正交码，跳频序列用于多址扩频通信，与光正交码有着密切的关系。Fuji-Hara，Miao和三岛发现了跳频序列与分块型差分填充之间的等价关系。Fuji-Hara，Miao和三岛利用这个等价性构造了许多最优跳频序列的无穷族，Miao还考虑了多址通信系统的安全性。课题涉及认证码、秘密共享方案、基于身份的签名方案和代理密码系统等，Fuji-Hara、Miao、三岛和Shinohara还对组合设计理论中与光正交码和跳频序列相关的几个课题进行了理论研究。少