Znanstveni kolokviji
On Rings, Weights, Codes, and Isometries
Vrijeme: 
20.5.2015 17:00 
Predavaonica: 
005 
Predavač: 
Marcus Greferath Aalto University, Finland 
Naziv: 
On Rings, Weights, Codes, and Isometries 
Opis:
It has been apparent since the end of the foregoing century that finite Frobenius rings (and modules) are the adequate alphabets for ringlinear 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 nonHamming weights have played a prominent role in ringlinear 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 ringlinear coding theory. He died in November 2014.

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