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

光学代码多访问通信中使用光学正交代码，因此多个用户可以在一个单个光学通道中有效传输和接收信息。众所周知，最佳的光学正交代码等效于一种称为最大循环T差填料的组合结构。 The main purpose of this research project is to construct optimal optical orthogonal codes from a combinatorial approach, that is, instead of constructing optimal 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 materies, and used them to construct many cyclic t-difference packings with maximum 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 asymmetric optimal光学正交代码。通过与光学正交代码密切相关的多访问传播频率序列。Fuji-Hara，Miao和Mishima发现了频率跳跃序列与分区类型差异包装之间的等效关系。通过使用这种等效性，富士，米奥和米希马（Miao）和米希马（Mishima）构建了许多最佳频率跳跃序列的无限家族。涵盖的主题包括身份验证代码，秘密共享方案，基于ID的签名方案以及代理密码系统。Fuji-Hara，Miao，Mishima，Mishima和Shinohara还对组合设计理论中的几个主题进行了理论研究，这些研究与光学的正交代码和频率希望序列相关。较少的