On the Constructions of Optical Orthogonal Codes from Combinatorial Design Theory

光正交码用于光码分多址通信，使得多个用户可以在一个光信道上高效地发送和接收信息。众所周知，最优光正交码等价于一种称为最大循环t-差填充的组合结构。本研究的主要目的是通过一种组合方法来构造最优光正交码，即不是直接构造最优光正交码，而是构造其相应的最大循环t-差包装。Fuji-Hara，Miao和Mishima引入了不完全循环差矩阵的新概念，并利用它们构造了许多具有最大块数的循环t-差包装。结合计算机搜索，构造了许多无穷族的最佳光正交码。权值为4，相关约束为1，码长为v…的最优光正交码的存在性Shinohara利用有限几何中特殊的弧形和锥形构造了光正交码，得到了无穷族的渐近最优光正交码。跳频序列用于与光正交码密切相关的多址扩频通信中。Fuji-Hara，Miao和Mishima发现了跳频序列和分割型差分包装之间的等价关系。利用这种等价性，Fuji-Hara，Miao和Mishima构造了许多最佳跳频序列的无限族，Miao还考虑了多址通信系统的安全性。内容包括认证码、秘密共享方案、基于身份的签名方案和代理密码体制。Fuji-Hara、Miao、Mishima和Shinohara还对与光正交码和跳频序列相关的组合设计理论中的几个主题进行了理论研究。较少

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