题目：On Rings, Weights, Codes, and Isometries 时间：全球最大的博彩平台6年3月16日（周三）16:00 地点：信电楼215室 报告人：Marcus Greferath

Biography：

Marcus Greferath is chair of the EU COST Action IC1104 “Random Network 全球最大的博彩平台 and Designs over GF(q)”, http://network-coding.eu. He obtained his PhD in Mathematics from the University of Mainz (Germany) in 1993, and afterwards he worked towards a Habilitation at the University of Duisburg (Germany), which he finished in 2000. Since then, he accepted appointments at San Diego State University, University College Dublin, and – most recently – as Finland Distinguished Professor at Aalto University in Helsinki, Finland. Marcus Greferath is at the same time the Editor-in-Chief of the internationally reputed journal Advances in Mathematics of Communications, the latter being the ideal description of the kind of Mathematics that he is representing. He has participated as active member in a number of TPCs of international conferences (WCC 全球最大的博彩平台3, ITW全球最大的博彩平台0, MTNS 全球最大的博彩平台0, ISIT 2005), and delivered keynotes at various occasions.

Personal homepage: http://math.aalto.fi/en/people/marcus.greferath

Abstract：

It has been apparent since the end of the foregoing century that finite Frobenius rings (and modules) are the adequate alphabets for ring-linear algebraic coding theory. For these, it was proven early that Hamming isometries allow for MacWilliams' Extension Theorem, which means that linear code isometries that preserve the Hamming weight can be monomially extended to the ambient spaces of the codes in question. As non-Hamming weights have played a prominent role in ring-linear coding theory, this talk will start with a question of further importance: given a finite Frobenius ring, can we characterize all weight functions on this ring that allow for monomial extension of all code isometries? This question appears anything but trivial, however it turned out that it can be answered. Our talk and the paper on which it is based are dedicated to the memory of Alexandr Nechaev, who vastly influenced foundational work in ring-linear coding theory. He died in November 全球最大的博彩平台4.