Discrete Mathematics Problems Arising in Sequence Design for Digital Communications

序列相关特性的研究始于20世纪50年代，在现代数字传输系统中，包括码分多址、多载波无线传输、雷达信息处理和光时域反射等，仍然具有核心重要性。本研究计划的目的是研究这一领域的某些经典问题，这些问题的最新成果为研究开辟了新的方向。这包括相互低相关序列集的设计和分析，优点因子问题，Golay互补对的构造和枚举，以及广义Barker序列问题。一般的科学方法将是结合离散数学、数字通信工程和计算科学的工具和见解。在适当的情况下，实验计算将用于揭示模式，识别关键示例，提高直觉，从而为新的理论结果指明道路。

The study of the correlation properties of sequences began in the 1950s and continues to be of central importance in modern digital transmission systems, including code-division multiple access, multicarrier wireless transmission, radar information processing, and optical time domain reflectometry. The objectives of the research plan are to study particular classical problems in this area for which recent results have opened up new research directions. This includes the design and analysis of sequence sets with mutually low correlation, the merit factor problem, the construction and enumeration of Golay complementary pairs, and the generalised Barker sequence problem. The general scientific approach will be to combine tools and insights from discrete mathematics, digital communications engineering, and computing science. Where appropriate, experimental computation will be used to reveal patterns, identify key examples, improve intuition, and so point the way to new theoretical results.