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Algebraic Coding Theory
MATH 4012 Spring 2026
Dr. Hunter Lehmann
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\(\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\cC}{\mathcal{C}} \newcommand{\F}{\mathbb{F}} \newcommand{\GF}{\mathrm{GF}} \DeclareMathOperator{\Span}{Span} \newcommand{\transpose}[1]{#1^{\top}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Course Documents
Syllabus
Course Information
My Philosophy
Course Structure
Course Grading
Course Websites
Other Course Policies
Grading Specifications
General Expectations for All Work
Significant Errors and Minor Errors
Specifications for Assignments
Engagement Credit Items
Specifications for Exams
Specifications for the Video Project
Course Resources
Calculation Tools
Matrices over Finite Fields
Definitions
Definitions
Course Notes
Week 1
Tuesday 1/13
Thursday 1/15
Week 2
Tuesday 1/20
Thursday 1/22
Week 3
Tuesday 1/27
Thursday 1/29
Daily Prep Activities
Daily Prep 2
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Exercises
Daily Prep 3
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Exercises
Daily Prep 4
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Exercises
Daily Prep 5
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Daily Prep 6
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
In-Class Activities
Introduction to Codes
Distance of a Code and Error Correction
The Hamming Code
Linear Algebra with Finite Fields
Linear Codes
1-Error Correcting Codes
Weekly Practice
Weekly Practice 1
Weekly Practice 2
Weekly Practice 3
Problem Sets
Problem Set M1
Algebraic Coding Theory
MATH 4012 Spring 2026
Dr. Hunter Lehmann
School of Mathematics
Georgia Institute of Technology
Last Updated: January 29, 2026
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