Algebraic Structures in Coding Theory

Department: 
MATH
Course Number: 
4012
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
no regular schedule

Introduction to linear error correcting codes with an emphasis on the algebraic tools required, including matrices, vector spaces, groups, polynomial rings, and finite fields.

Prerequisites: 

MATH 1502

Course Text: 

No text

Topic Outline: 
  • Fundamentals of Error Correcting, Codes Block codes, Hamming distance, error correction.
  • Linear Codes Generator and parity-check matrices, dual codes, Hamming and other perfect codes, standard array decoding.
  • Special Linear Codes, Reed Muller codes, self-dual codes, binary Golay codes.
  • Finite fields Irreducible polynomials, minimum polynomials, properties of finite fields.
  • Cyclic Codes Rings and ideals, cyclic subspaces, generating polynomials, syndrome decoding, burst error decoding.
  • BCH Codes - BCH codes and BCH bounds, the Euclidean algorithm and decoding BCH codes.
  • Error Correction, Techniques Reed Solomon codes, channel erasures, BCH codes with erasures, interleaving.