WEEK |
DATES |
ASSIGNMENTS |
TOPICS |
~ |
Jan. 5-6 |
~ |
Introduction to the course. What is coding theory. Basics of finite fields. |
1 |
Jan. 9-13 |
~ |
Linear codes. Symmetric and Gaussian channels. Capacity. |
2 |
Jan. 16-20 |
~ |
Decoding linear codes. Bounds. |
3 |
Jan. 23-27 |
A1 out: Jan. 24 |
2-error-correcting BCH codes. Finite fields. Polynomials. |
4 |
Jan. 30 - Feb. 3 |
~ |
Review: rings, fields and ideals.
Extension fields. Splitting fields. |
5 |
Feb. 6-10 |
~ |
Characterization of finite fields: subfield
criterion, primitive elements, Gauss algorithm. |
6 |
Feb. 13-17 |
A1 in / A2 out: Feb. 14 |
Characterization of finite fields (cont):
irreducible polynomials; number and properties. |
~ |
Feb. 20-24 |
~ |
Reading Week (No Classes). |
7 |
Feb. 27 - Mar. 3 |
~ |
Roots of irreducibles; traces and norms. |
8 |
Mar. 6-10 |
A2 in / A3 out: Mar. 7 |
Finding irreducible polynomials. Factorization
of polynomials and applications. |
9 |
Mar. 13-17 |
Midterm test: Mar. 16 |
Squarefree, distinct-degree and equal-degree
factorization. |
10 |
Mar. 20-24 |
~ |
Cyclic codes. Minimal polynomials. |
11 |
Mar. 27-31 |
A3 in: Mar. 28 |
Computing minimal polynomials. Hamming and
BCH codes revisited; t-error correcting BCH codes.
|
12 |
Apr. 3-6 |
Project in: Apr. 4 |
Reed-Solomon codes. Review of course.
Comments on final exam. Oral presentations. |