Coding theory is an interdisciplinary area
whose goal is to study the properties of various types of codes and
design methods of error detection and error correction. In the first
part of this talk, we give a quick introduction to linear codes and
define the concept of Hamming distance and show how it can be used to
perform error correction. In the second part, we introduce a few
concepts from commutative algebra such as Hilbert series and Fitting
modules. Then, we show that one can naturally assign a Fitting module
to a linear code and recover the minimum distance of the linear code
from the homological data of the module. This is a joint work with
Stefan Tohaneanu.
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