报告一：Tor Helleseth

报告题目：50 years history of the cross correlation between m-sequences

报告人：Professor Tor Helleseth University of Bergen

主持人：李成举  

报告时间：2019年11月26日 14：30-15：30

报告地点：理科大楼B1102

报告摘要：

Maximum-length sequences (or m-sequences) of period 2^m-1 are generated by a linear feedback shift register of degree m. These sequences have many important applications in modern communication systems. The most well known property of m-sequences is their well-known two-level ideal autocorrelation. The first major result on the cross correlation is the determination of the cross correlation between the m-sequences used in constructing the famous Gold sequences that was published 50 years ago in January 1968. During the last 50 years the cross correlation between m-sequences of the same period has been intensively studied by many research groups. Many important results have been obtained but still many open problems remain in this area. This talk will give an updated survey of the status of the cross correlation of m-sequences as well as some consequences of these results.

周期为2^m-1的最大长度序列(或m序列)是由m次线性反馈移位寄存器产生的。这些序列在现代通信系统中有许多重要的应用。m序列最著名的性质是众所周知的两值理想自相关。第一个主要结果是确定了50年前1968年1月发表的构造著名Gold序列所用的m序列之间的互相关值。近50年来，m序列间的相互关系已被许多研究小组深入研究。虽然取得了许多重要的研究成果，但仍存在许多有待解决的问题。本次报告介绍m序列的互相关值的现状与相关结果。

报告人简介：

Tor Helleseth (IEEE Fellow) received his Dr. Philos. degree in mathematics from the University of Bergen, Norway, in 1979. During the academic years 1977-1978 and 1992-1993 he was on sabbatical leave at the University of Southern California, USA, and during 1979-1980 he was a Postdoctoral fellow at the Eindhoven University of Technology, The Netherlands. From 1981 to 1984 he was a researcher at the Chief Headquarters of Defense in Norway. Since 1984 has he has been Professor at the Department of Informatics, University of Bergen. He served as an Associate Editor for IEEE Transactions on Information Theory, 1991-1993 for Coding Theory and 2012-2014 for Sequences. He is on the editorial board for Designs, Codes and Cryptography (DCC), and Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences (CCDS). He has published more than 350 papers in international refereed journals and conferences in coding theory, cryptography and sequence designs, including more than 100 co-authors from more than 25 countries. He was the program co-chair for Eurocrypt’93, IEEE Information Theory Workshop, ITW1997, ITW2007, Arctic Crypt 2016 and for Sequences and Their Applications, SETA’98, SETA’04, SETA’06, SETA’12 and SETA’18. Professor Helleseth was a coordinator of NISNet, a national network in information security, in Norway 2007-2011. In 1997 he was elected IEEE Fellow for his "Contributions to Coding Theory and Cryptography" and in 2004 elected member of the Norwegian Academy of Science (Det Norske Videnskaps-Akademi). He served on the Board of Governors for the IEEE IT-Society during 2007-2009. His interests include coding theory, cryptography, sequence designs, finite fields and discrete mathematics.

Tor Helleseth (IEEE Fellow)在1979年获挪威卑尔根大学数学博士学位。1979-1980年期间，他是荷兰Eindhoven理工大学的博士后研究员。1981-1984年期间，他是挪威国防总部的研究员。自1984年以来，他一直是卑尔根大学信息学系的教授。担任《IEEE Transactions on Information Theory》副编辑，1991-1993年负责编码理论，2012-2014年，负责序列。他是《Designs, Codes and Cryptography》(DCC)和《Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences》(CCDS)的编辑委员会成员。他在编码理论、密码学和序列设计方面的国际期刊和会议上发表了350多篇论文，包括来自25个国家的100多名合作者。他曾担任Eurocrypt ' 93、 ITW1997、ITW2007、Arctic Crypt 2016以及SETA ' 98、SETA ' 04、SETA ' 06、SETA ' 12和SETA ' 18 的联合主席。Helleseth教授是2007-2011年挪威国家信息安全网络NISNet的协调员。1997年，他因为对编码和密码的贡献被选为IEEE会士，2004年，他被选为挪威科学院院士。2007-2009年期间，他担任IEEE IT协会的理事会成员。他的研究兴趣包括编码理论、密码学、序列设计、有限域和离散数学。

报告二：Patrick Solé

报告题目：Two recent results on additive quaternary codes

报告人：Professor  Patrick Solé    University of Paris 8

主持人：李成举  

报告时间：2019年11月26日 15：30-16：30

报告地点：理科大楼B1102

报告摘要：

Additive codes are codes over GF(4) that are closed under addition but not under scalar multiplication. We show that the punctured dodecacode  is  uniformly packed solving an open problem from 1974 (joint work with Shi and Krotov). We prove that additive cyclic codes are asymptotically good (joint work with Shi and Wu).

加性码是在GF(4)上的码，它在加法下是封闭的，而在标量乘法下是不封闭的。我们证明了穿孔十二进制码是均匀压缩码，解决了1974年的一个开放问题(与Shi和Krotov的联合工作)。我们证明了加性循环码是渐近好的(与Shi和Wu的联合工作)。

报告人简介：

巴黎第八大学教授，国际著名的代数编码与密码学专家。研究领域包括代数组合、代数图论、代数编码、离散数学、格的构造、模形式等。目前已在国际著名期刊《IEEE Transaction on Information Theory》, 《Finite Fields and Their Applications》, 《Journal of Algebra》, 《Journal of Combinatorial Theory Series B》, 《Bulletin of the American Mathematical Society》 等发表170余篇专业学术论文，在国际学术会议上发表论文70余篇，出版英文专著3本。1995年，与其合作者撰写的论文“The linearity of Kerdock, Preparata, Goethals, and related codes”获信息论方面的最佳论文奖, 已经被他引1300余次。曾担任《IEEE Transactions on Information Theory》副编辑，目前担任多个SCI期刊编委。

报告三：施敏加

报告题目：On one symbol-pair cyclic codes

报告人：施敏加教授  安徽大学

主持人：李成举  

报告时间：2019年11月26日 16：30-17：30

报告地点：理科大楼B1102

报告摘要：

The symbol-pair metric was introduced by Cassuto and Blaum in 2010 in connection with symbol-pair channels. In this note, we present a new combinatorial characterization for the symbol-pair weight by run of $0$'s of length $i$, and study three classes of one symbol-pair weight cyclic codes. The arguments are based on properties of two different notions of runs. The symbol run for the first two classes, and a burst error type of run in the case of two-dimensional cyclic codes. An extension of the first two constructions to codes for $b$-symbol read channels introduced by Yaakobi et al. in 2016 is sketched out.

在这次讨论中，本文提出了一种新的符号对权重的组合特征，并研究了三类单符号对权重循环码。这些论点基于两种不同的运行，即：前两类的符号运行，以及在二维循环码的情况下的突发错误类型的运行。

报告人简介：

施敏加，教授，博士研究生导师，基础数学系主任，安徽省学术与技术带头人，曾获安徽省自然科学一等奖与第二届“安徽省青年数学奖”。主持国家自然科学基金3项，安徽省自然科学基金杰出青年基金等省部级重点项目5项。出版英文专著2本，在《IEEE Transaction on Information Theory》、《Designs, Codes and Cryptography》、《Finite Fields and Their Applications》等国内外重要学术期刊上发表学术论文80余篇，其中 SCI检索60余篇。曾应邀访问法国，新加坡等国家。