7月16日:向青/岳勤/張耀祖/李崇道
發布時間:2019-07-10  閱讀次數:1883

報告一:向青

 

報告題目:Fourier analysis on finite abelian groups and uncertainty principles 
報 告 人: 向青 
教授  美國特拉華大學
主 持 人: 李成舉 副教授
報告時間:2019年7月16日 周二 14:00-15:00
報告地點:理科大樓B1202

 

報告摘要:
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 $G$.
報告人簡介:
向青,1995獲美國 Ohio State University博士學位, 現為美國特拉華大學(University of Delaware)教授。主要研究方向為組合設計、有限幾何、編碼和加法組合。現為國際組合數學界權威期刊《The Electronic Journal of Combinatorics》主編,同時擔任SCI期刊《Designs, Codes and Cryptography》, 《Journal of Combinatorial Designs》的編委。曾獲得國際組合數學及其應用協會頒發的杰出青年學術成就獎—Kirkman Medal。在國際組合數學界最高級別雜志《J. Combin. Theory Ser. A》,《J. Combin. Theory Ser. B》,  《Combinatorica》,以及《Trans. Amer. Math. Soc.》,《IEEE Trans. Inform. Theory》等重要國際期刊上發表學術論文80余篇。主持完成美國國家自然科學基金、美國國家安全局等科研項目10余項。曾在國際學術會議上作大會報告或特邀報告50余次。

 

報告二:岳勤

 

報告題目:LCD and Self-Orthogonal Group Codes in a Finite Abelian p-Group Algebra
報 告 人: 岳勤
教授  南京航空航天大學
主 持 人: 李成舉 副教授
報告時間:2019年7月16日 周二 15:00-16:00
報告地點:
理科大樓B1202


報告摘要: 
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).
報告人簡介:
岳勤,南京航空航天大學數學系教授,博士生導師。1999年中國科學技術大學數學系博士學位,師從馮克勤教授。曾訪問過意大利、韓國、香港和臺灣等地。研究方向為代數數論,代數K理論,和代數編碼理論研究,發表SCI論文70余篇,其中包括:J. Reine Angew. Math., Math. Z, IEEE Trans. Inform. Theory等刊物,主持4項國家自然科學基金和2項國際合作項目,江蘇省青藍工程學科帶頭人。

 

報告三:張耀祖

 

報告題目:Algebraic decodings of the binary quadratic residue codes
報 告 人:  張耀祖
教授  臺灣義守大學
主 持 人:  李成舉 副教授
報告時間:2019年7月16日 周二 16:00-17:00
報告地點:
理科大樓B1202

 

報告摘要:

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. 
報告人簡介:

張耀祖臺灣義守大學教授、博導,臺灣東吳大學(Soochow University)數學學士,臺灣清華大學(Tsing-Hua University)數學碩士,美國密歇根大學(University of Michigan-Ann Arbor)數學博士。指導5名博士生獲得博士學位,其中3人在大學任教(兩名現職教授、一名副教授),另外兩人就職科技公司研發單位。獲得14項國內外專利(其中美國專利2件、大陸專利3件,其余為臺灣專利)。發表SCI學術期刊論文30篇(其中IEEE期刊14篇,4篇在旗艦期刊Transactions on Information Theory、3篇在Transactions on Communications)。義守大學編碼團隊在平方剩余碼譯碼方面領先世界、取得世界性的成果(完成六個不同碼長平方剩余碼譯碼算法)。2007年提出世界最快的“3C譯碼器”(其譯碼速度比當時業界提供數據快100倍),獲得臺灣、大陸、美國三地專利。

 

報告四:李崇道

 

報告題目:Minimum-Degree Perfect Gaussian Integer Sequences From Monomial o-Polynomials
報 告 人: 李崇道
教授  臺灣義守大學
主 持 人: 李成舉 副教授
報告時間:2019年7月16日 周二 17:00-18:00
報告地點:
理科大樓B1202

 

報告摘要:

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. 
報告人簡介:

李崇道,臺灣義守大學教授,IEEE Senior Member,獲得6項專利,發表SCI學術期刊論文30篇,其中IEEE期刊22篇,8篇在旗艦期刊Transactions on Information Theory、5篇在Transactions on Communications、7篇在Communications Letters、2篇在Signal Processing Letters),獲得科技部電信學門個人專題計劃(2008-2019),補助總額920萬元。擔任IEEE Information Theory Society Tainan Chapter副主席(2017-2018),兼任義守大學圖書與咨訊處副處長 (2018-present)。

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