Discrete Mathematics Problems Arising in Sequence Design for Digital Communications

对序列相关性的研究始于20世纪50年代，并且在现代数字传输系统中仍然具有核心重要性，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计。该研究计划的目标是研究这一领域的特定经典问题，最近的研究结果开辟了新的研究方向。这包括设计和分析的序列集相互低相关性，品质因子问题，建设和列举的Golay互补对，和广义巴克序列问题。一般的科学方法将是结合联合收割机工具和离散数学，数字通信工程和计算科学的见解。在适当的情况下，实验计算将被用来揭示模式，识别关键的例子，提高直觉，并指出新的理论结果的方式。

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.