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日期：2025-03-21
来源：数理学院
题目：Large Sets of Quasi-Complementary Sequences From Polynomials over Finite Fields and Gaussian Sums
主讲：衡子灵 教授
时间：3月25日15:50
地点：文理楼B302
主办：数理学院
主讲嘉宾简介：
衡子灵，长安大学教授、博士生导师。2017年博士毕业于南京航空航天大学基础数学专业；2017年7月-2018年7月在香港科技大学任博士后；2018年7月至今在长安大学工作。主要研究代数编码理论，在《IEEE Transactions On Information Theory》、《Journal of Algebra》、《Designs, Codes and Cryptography》等期刊上发表SCI论文45篇，主持两项国家级科研项目和多项省级项目，入选陕西省三秦英才特殊支持计划青年拔尖人才、陕西省科协青年人才托举计划。
报告主要内容：
Perfect complementary sequence sets (PCSSs) are widely used in multi-carrier code-division multiple-access (MC-CDMA) communication system. However, the set size of a PCSS is upper bounded by the number of row sequences of each two-dimensional matrix in the PCSS. Then quasi-complementary sequence set (QCSS) was proposed to support more users in MC-CDMA communications. For practical applications, it is desirable to construct an $(M,K,N,\vartheta_{max})$-QCSS with $M$ as large as possible and $\vartheta_{max}$ as small as possible, where $M$ is the number of matrices with $K$ rows and $N$ columns in the set and $\vartheta_{max}$ denotes its periodic tolerance. There exists a tradeoff among these parameters and constructing QCSSs achieving or nearly achieving the known correlation lower bound has been an interesting research topic. Up to now, only a few constructions of asymptotically optimal or near-optimal periodic QCSSs were reported in the literature. In this talk, we construct five families of asymptotically optimal or near-optimal periodic QCSSs with large set sizes and low periodic tolerances. These families of QCSSs have set size $\Theta(q^2)$ or $\Theta(q^3)$ and flock size $\Theta(q)$, where $q$ is a power of a prime. To the best of our knowledge, only three known families of periodic QCSSs with set size $\Theta(q^2)$ and flock size $\Theta(q)$ were constructed and most of other known periodic QCSSs have set sizes much smaller than $\Theta(q^2)$. Our new constructed periodic QCSSs with set size $\Theta(q^2)$ and flock size $\Theta(q)$ have better parameters than known ones. They have larger set sizes or lower periodic tolerances. The periodic QCSSs with set size $\Theta(q^3)$ and flock size $\Theta(q)$ constructed by us have the largest set size among all known families of asymptotically optimal or near-optimal periodic QCSSs.
