This course covers the learning outcomes and goals of understanding codes from polynomials over finite fields. It teaches skills such as communication over a noisy channel, coding theory basics, Reed-Solomon codes, Reed-Muller codes, Hamming weight enumerator, algebraic geometry codes, and more. The teaching method includes theoretical explanations, examples, and conjectures. The intended audience for this course is individuals interested in coding theory, combinatorial coding theory, and algebraic geometry codes.
Overview
Syllabus
Intro
Communication over a Noisy Channel
Coding Theory Basics
Main Problem in Combinatorial Coding Theory
Tables for Linear Codes (codetables.de)
Reed-Solomon Codes are MDS
Doubly Extended (Projective) Reed-Solomon Codes
Reed-Solomon Code: Example 2
Main Conjecture for MDS Codes Ill
More Variables. Reed-Muller Codes
Reed-Muller Codes II
The Hamming Weight Enumerator of a Code Definition
Quadratic Polynomials in 2 Variables
Reed-Muller Codes from Cubic Curves
Reed-Muller Codes from Quartic Curves
Rational Point Counts for Quartic Curves: Asymmetry Definition
The Dual Code of a Linear Code
The MacWilliams Identity
Algebraic Geometry Codes
Codes to Communication
Taught by
Joint Mathematics Meetings
