Error-correcting codes are used to improve the reliability of information transmission. This course in an introduction to the mathematical theory of error correcting codes, covering algebraic and combinational methods used in designing good codes, and decoding algorithms. Topics selected from groups, rings, finite fields, vector spaces over finite fields, encoding and decoding of linear codes, bounds on the minimum distance, weight enumerators, perfect codes, Hamming codes, MDS codes, Golay codes, Reed-Muller codes, cyclic codes, and quadratic residue codes.
Prerequisites: MATH 1503; and MATH 2203 or CS 1303 or consent of the instructor. |
