7月16日:向青/岳勤/张耀祖/李崇道
发布时间:2019-07-10  阅读次数:3448

报告一:向青

 

报告题目:Fourier analysis on finite abelian groups and uncertainty principles 
报 告 人: 向青 
教授  美国特拉华大学
主 持 人: 李成举 副教授
报告时间:2019年7月16日 周二 14:00-15:00
报告地点:理科大楼B1202

 

报告摘要:
Let $G$ be a finite abelian group. If $f: G\rightarrow {\bf C}$  is a nonzero function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle states that $|\supp(f)||\supp(\hf)|\geq |G|$. The purpose of this talk is twofold. First, we present the shift bound for abelian codes with a streamlined proof. Second, we use the shifting technique to prove a generalization and a sharpening of the Donoho-Stark uncertainty principle. In particular, the sharpened uncertainty principle states, with notation above, that $$|\supp(f)||\supp(\hf)|\geq |G|+|\supp(f)|-|H(\supp(f))|,$$ where $H(\supp(f))$ is the stabilizer of $\supp(f)$ in $G$.
报告人简介:
向青,1995获美国 Ohio State University博士学位, 现为美国特拉华大学(University of Delaware)教授。主要研究方向为组合设计、有限几何、编码和加法组合。现为国际组合数学界权威期刊《The Electronic Journal of Combinatorics》主编,同时担任SCI期刊《Designs, Codes and Cryptography》, 《Journal of Combinatorial Designs》的编委。曾获得国际组合数学及其应用协会颁发的杰出青年学术成就奖—Kirkman Medal。在国际组合数学界最高级别杂志《J. Combin. Theory Ser. A》,《J. Combin. Theory Ser. B》,  《Combinatorica》,以及《Trans. Amer. Math. Soc.》,《IEEE Trans. Inform. Theory》等重要国际期刊上发表学术论文80余篇。主持完成美国国家自然科学基金、美国国家安全局等科研项目10余项。曾在国际学术会议上作大会报告或特邀报告50余次。

 

报告二:岳勤

 

报告题目:LCD and Self-Orthogonal Group Codes in a Finite Abelian p-Group Algebra
报 告 人: 岳勤
教授  南京航空航天大学
主 持 人: 李成举 副教授
报告时间:2019年7月16日 周二 15:00-16:00
报告地点:
理科大楼B1202


报告摘要: 
Let Fq be a finite field with q elements and p be a prime with gcd( p, q) = 1. Let G be a finite abelian p-group and Fq(G) be a group algebra. In this paper, we find all primitive idempotents and minimal abelian group codes in the group algebra Fq (G). Furthermore, we give all LCD abelian codes (linear code with complementary dual) and self-orthogonal abelian codes of Fq (G).
报告人简介:
岳勤,南京航空航天大学数学系教授,博士生导师。1999年中国科学技术大学数学系博士学位,师从冯克勤教授。曾访问过意大利、韩国、香港和台湾等地。研究方向为代数数论,代数K理论,和代数编码理论研究,发表SCI论文70余篇,其中包括:J. Reine Angew. Math., Math. Z, IEEE Trans. Inform. Theory等刊物,主持4项国家自然科学基金和2项国际合作项目,江苏省青蓝工程学科带头人。

 

报告三:张耀祖

 

报告题目:Algebraic decodings of the binary quadratic residue codes
报 告 人:  张耀祖
教授  台湾义守大学
主 持 人:  李成举 副教授
报告时间:2019年7月16日 周二 16:00-17:00
报告地点:
理科大楼B1202

 

报告摘要:

Quadratic residues (QR) codes, introduced by Prange in 1958, are cyclic codes with code rates not less than 1/2 and generally have large minimum distances, so that most of the known QR codes are the best-known codes. Both the famous Hamming code of length 7 and the Golay codes are QR codes. However, it is difficult to decode QR codes, and except for those of low lengths, the decoders for QR codes appeared quite late. The first algebraic decoder of Golay code of length 23 was proposed by Elia in 1987. From 1990, Reed et al. published a series of papers about algebraic decoding of QR codes of lengths 31, 41, 47, and 73. After that, the coding group of I-Shou University continued the QR decoding study and developed decoders of lengths 71, 79, 89, 97, 103, and 113. Hence, all binary QR codes of lengths not exceed 113 are decoded. In this presentation, we give a brief review of decoding QR codes. It also includes the most recent works done by I-Shou coding group which improve the decoding processes for the practical hardware implementation. 
报告人简介:

张耀祖台湾义守大学教授、博导,台湾东吴大学(Soochow University)数学学士,台湾清华大学(Tsing-Hua University)数学硕士,美国密歇根大学(University of Michigan-Ann Arbor)数学博士。指导5名博士生获得博士学位,其中3人在大学任教(两名现职教授、一名副教授),另外两人就职科技公司研发单位。获得14项国内外专利(其中美国专利2件、大陆专利3件,其余为台湾专利)。发表SCI学术期刊论文30篇(其中IEEE期刊14篇,4篇在旗舰期刊Transactions on Information Theory、3篇在Transactions on Communications)。义守大学编码团队在平方剩余码译码方面领先世界、取得世界性的成果(完成六个不同码长平方剩余码译码算法)。2007年提出世界最快的“3C译码器”(其译码速度比当时业界提供数据快100倍),获得台湾、大陆、美国三地专利。

 

报告四:李崇道

 

报告题目:Minimum-Degree Perfect Gaussian Integer Sequences From Monomial o-Polynomials
报 告 人: 李崇道
教授  台湾义守大学
主 持 人: 李成举 副教授
报告时间:2019年7月16日 周二 17:00-18:00
报告地点:
理科大楼B1202

 

报告摘要:

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. 
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)。

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