Aug 08, 2025  
OHIO University Graduate Catalog 2022-23 
    
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MATH 6231 - Coding Theory I

A mathematically rigorous survey of Error-Correcting Codes with emphasis on their parameters and their algorithmic efficiency for coding and decoding. Reed Solomon Codes, Goppa Codes, Reed Muller Codes, Algebraic Geometry Codes. Coding and Decoding based on Fast Fourier Transform algorithms. This course surveys various approaches to the structure theory of convolutional codes. They are considered as vector spaces over fields of Laurent expansions, as modules over rings of polynomials and as graph codes. All necessary algebraic background beyond linear algebra is presented in the class, including concepts related to modules over principal ideal domains and ideas regarding trellises and other relevant types of graphs.

Requisites: MATH 5230
Credit Hours: 4
Repeat/Retake Information: May not be retaken.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes:
  • After completing both Coding Theory I and II students will acquire a panoramic background of the various aspects of the theory of Error-Correcting Codes and their Applications.


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