Mathematics Colloquium | From Linear Codes to Noncommutative Algebra, March 28

The Mathematics Colloquium series features Miodrag Iovanov from the University of Iowa discussing "From Linear Codes to Noncommutative Algebra" on Tuesday, March 28, from 4-5 p.m. via Zoom .

Abstract: One of the landmark results that sits at the foundations of a part of coding theory is MacWilliams' Extension Theorem on linear codes. A linear code can classically be defined simply as a linear subspace of the n-dimensional vector space over the field with two elements. Codes have quickly proved to be useful over other finite fields and even finite rings, at which point it became clear, through work of J.A.Wood, that the above mentioned fundamental property is very tightly related to the notion of Frobenius algebras. Frobenius rings go back to work of - well, Frobenius - as well as Nakayama, and play a central role in groups and quantum groups. It turns out that the categorical properties of these rings are still tightly related to a general version of the Extension property, which can be rephrased in homological terms. These general considerations (of "Infinite Linear Codes") lead to some surprising new results in non-commutative rings, tied to work of S. Lopez-Permouth and others.  

homological terms. These general considerations (of "Infinite Linear Codes") lead to some surprising new results in non-commutative rings, tied to work of S. Lopez-Permouth and others.