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Algebraic Coding Theory
MATH 4012 Spring 2026
Dr. Hunter Lehmann
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\(\require{mathtools}\newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\cC}{\mathcal{C}} \newcommand{\F}{\mathbb{F}} \newcommand{\GF}{\mathrm{GF}} \DeclareMathOperator{\Span}{Span} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\rk}{rk} \DeclareMathOperator{\wt}{wt} \newcommand{\transpose}[1]{#1^{\top}} \newcommand{\by}{\mathbf{y}} \newcommand{\bc}{\mathbf{c}} \newcommand{\bx}{\mathbf{x}} \newcommand{\bm}{\mathbf{m}} \newcommand{\bs}{\mathbf{s}} \newcommand{\be}{\mathbf{e}} \newcommand{\bh}{\mathbf{h}} \DeclarePairedDelimiter\floor{\lfloor}{\rfloor} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \newcommand{\fillinmath}[1]{\mathchoice{\underline{\displaystyle \phantom{\ \,#1\ \,}}}{\underline{\textstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptscriptstyle\phantom{\ \,#1\ \,}}}} \)
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 Calendar
Video Project
Video Project Requirements
Team Contract
Report
Peer Review
Deadlines
Course Resources
Calculation Tools
Matrices over Finite Fields
Bounds
Definitions and Algorithms
Definitions
Algorithms
Results
Results
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
Week 4
Tuesday 2/3
Thursday 2/5
Week 5
Tuesday 2/10
Thursday 2/12
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
Daily Prep 7
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Important Terms
Daily Prep 8
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Important Terms
Daily Prep 9
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Important Terms
Daily Prep 10
Learning Objectives
Basic Learning Objectives
Advanced Learning Objectives
Resources for Learning
Important Terms
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
Decoding Linear Codes
Bounds on Codes
The Gilbert-Varshamov Bound
Irreducible Polynomials & Building Finite Fields
Weekly Practice
Weekly Practice 1
Weekly Practice 2
Weekly Practice 3
Weekly Practice 4
Weekly Practice 5
Problem Sets
Problem Set M1
Problem Set M2
Problem Set M3
Algebraic Coding Theory
MATH 4012 Spring 2026
Dr. Hunter Lehmann
School of Mathematics
Georgia Institute of Technology
Last Updated: February 19, 2026
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