On Perfect Difference Families and their Applications to Radar Arrays

完全差分族是在1970年中期作为射电天文学中间隔可移动天线问题的抽象而引入的。雷达阵列作为空间可移动天线问题的推广被引入到高维空间以跟踪和控制飞艇。本研究利用组合设计理论，构造了许多完全差分族及相关结构，如雷达阵列、齐次一致差分矩阵和单调有向设计等。在数字内容版权保护中的跟踪算法方面也取得了新的成果。

Perfect difference families were introduced as an abstraction of the problem of spacing movable antennas in radio astronomy in the middle of 1970. Radar arrays were introduced as a generalization of the spacing movable antennas problem to high dimensions to track and control airships. In this research project, by using combinatorial design theory, many perfect difference families and related structures such as radar arrays, homogeneous uniform difference matrices and monotonic directed designs are constructed. New results are also obtained on tracing algorithms in digital contents copyright protection.