报告人: Prof. Dr. Marcus Greferath.   Dept. Mathematics and Systems Analysis Aalto University School of Science 题目: On Codes, Isometries, and Monomial Representations 地点:   知新楼B1032 时间:   2016年3月11日 上午11:00-11:50 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 is anything but trivial, however we have managed to answer it. 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 2014.