November Lectures
Week of November 4-8
Nov 4: Factorization of polynomials: applications, complete factorization
and squarefree factorization.
Nov 6: Comments about Assignment 3. Elimination of repeated factors.
Distinct-degree factorization. Equal-degree factorization (Cantor and Zassenhaus).
Week of November 11-15
Nov 11: Comments about Assignment 3. Equal-degree factorization (cont).
Cyclic codes: definition and examples.
Nov 13: Characterization of cyclic codes as ideals.
Generator polynomial and matrix.
Week of November 18-22
Nov 18: Minimal polynomials: definition and properties. Cyclotomic cosets;
examples.
[A3 handed in; A4 handed out.]
Nov 20: Cyclotomic cosets and factors of x^n - 1. Check polynomial and
parity check matrix. Hamming codes as examples of cyclic codes. Computing
minimal polynomials.
Week of November 25 - 29
Nov 25: 2-error-correcting BCH codes as example of cyclic codes.
Comments about Assignment 4. t-error-correcting BCH codes.
Nov 27: Designed distance and t-error-correcting BCH codes.
Examples.
Week of December 2
Dec 2:
Reed-Solomon codes. Course overview. Comments about the exam.
Dec 4: [A4 handed in.]
Dec 18: Course presentations (for graduate students).
Dec 19: Final exam.
To October lectures.