循环设计及其在通信中的应用

项目名称： 循环设计及其在通信中的应用

项目编号： No.11201114

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 单秀玲

作者单位： 河北师范大学

项目金额： 23万元

中文摘要： 组合设计理论研究的基本问题是确定离散结构（即设计）的构造方法和存在性。21世纪以来，计算机科学和信息科学发展迅猛，大量离散结构问题不断涌现，极大地促进了组合设计理论的飞速发展。因此，研究在现代通信中有重要应用的码类的组合特性和构造问题，已经成为当代组合设计领域的一个主流研究方向。本项目拟对严格v-循环填充设计、广义Kirkman方和可划分差族进行研究，力争给出新的构造方法，扩大已知结果。严格v-循环填充设计可用于构造二维光正交码，由于后者的良好自相关性和互相关性，在现代光纤通信、雷达声纳探测中着广泛的应用。广义Kirkman方可描述某些最优的双重恒重码。可划分差族可用于产生最优的常重复合码，并可用于构造跳频序列。这些都是近年来国内外组合设计界关注的焦点问题，因此对它们的研究有着重要的理论意义和应用价值。

中文关键词： 光正交码；可划分差族；正交阵列；超单设计；幻方

英文摘要： The basic problem of combinatorial design theory is the construction methods and the existence of discrete structures. Since 21 century, with the rapid development of computer and information sciences, many discrete structures spring up which stimulate the rapid development of combinatorial design theory. The study of combinatorial characters and constructions of codes which has important applications in morden communications become a main direction of morden combinatorial design theory. We will study strictly v-cyclic packing designs, generalized Kirkman squares and partitioned difference families. New constructions and new results are wanted. Strictly v-cyclic packing designs can give two-dimensional optical orthogonal codes with good aoto- and cross- correlation properties which can be used extensively in fiber-optical communications and radar sonar detections. Generalized Kirkman squares can descript some optimal constant weight codes. Partitioned difference families can used to obtain optimal constant composition codes and frequence hopping sequences. All of these are the focus of combinatorial design theory at home and abroad. So the study of them has important theoretical and applcation value.

英文关键词： Optical orthogonal code；Partitioned difference family；Orthogonal Array；Super-simple design；Magic squares