A survey on Algebraic Coding Theory, with a particular focus on how Polynomials over Finite Fields help us find efficient algorithms for encoding and decoding BCH Codes. Includes a coding scheme and noise simulator for BCH Codes that features several of the algorithms discussed in the literature.
Written by Ben Flin, Ben Sherwin, and Max Helman for MATH 4042 Intro to Modern Algebra II at Columbia University (Spring 2021).