讲座题目：Minimum-Degree Perfect Gaussian Integer Sequences From Monomial o-Polynomials 主讲人：李崇道 教授 主持人：李成举 副教授 开始时间：2019-07-16 17:00:00 结束时间：2019-07-16 18:00:00 讲座地址：中北校区理科楼B1202室 主办单位：计算机科学与软件工程学院
报告人简介： 李崇道，台湾义守大学教授，IEEE Senior Member，获得6项专利，发表SCI学术期刊论文30篇，其中IEEE期刊22篇，8篇在旗舰期刊Transactions on Information Theory、5篇在Transactions on Communications、7篇在Communications Letters、2篇在Signal Processing Letters），获得科技部电信学门个人专题计划(2008-2019)，补助总额920万元。担任IEEE Information Theory Society Tainan Chapter副主席(2017-2018)，兼任义守大学图书与咨讯处副处长 (2018-present)。 报告内容： A Gaussian integer is a complex number whose real and imaginary parts are both integers. A Gaussian integer sequence is called \textit{perfect} if it satisfies the ideal periodic auto-correlation functions. That is, let $\mathbf S=(s(0),s(1),\ldots,s(N-1))$ be a complex sequence of period $N$, where $s(t)=u(t)+v(t)i$ for $u(t),v(t)\in\mathbb{Z}$, and $i=\sqrt{-1}$.The complex sequence $\mathbf S$ is said to be a {\em perfect Gaussian integer sequence} if \begin{eqnarray} \label{Rsformula} R_{\mathbf S}(\tau)=\sum_{t=0}^{N-1} s(t){s^*(t+\tau)} \end{eqnarray} is nonzero for $\tau=0$ and is zero for any $1\leq \tau \leq N-1$, where $s^*$ denotes the conjugate of a complex number $s$. The \textit{degree} of a Gaussian integer sequence is defined to be the number of distinct nonzero Gaussian integers within one period of the sequence. In fact, its minimum degree is two. This study proposes a new construction method, called monomial o-polynomials, to generate the minimum-degree perfect Gaussian integer sequences. The resulting sequences have odd periods and high energy efficiency. Furthermore, the number of cyclically distinct perfect Gaussian integer sequences is shown. |
