MATHEMATICS 70.419/70.611, CLASS OUTLINE FOR FALL 2000

WEEK 

DATES 

ASSIGNMENTS 

SECTION/BOOK 

TOPICS 

1

Sep. 11-15

~

LN 8.1, p.305-309

Introduction to the course. What is coding theory. Basics of finite fields. Linear codes.

2

Sep. 18-22

A1 out: Sep. 20

LN 8.1, p.309-317

Decoding linear codes. Bounds.

3

Sep. 25-29

~

LN 8.2, p.317-317;
LN 1.2-1.3, p.11-22

Cyclic codes. Overview of BCH codes. Finite fields. Polynomials.

4

Oct. 2-5

A1 in / A2 out: Oct. 4

LN 1.3-1.4, p.23-27, 30-35

 Irreducible polynomials.
Extension fields.

5 

Oct. 10-13

~

LN 2.1, p.45-48

Characterization of finite fields.

6

Oct. 16-20

A2 in / A3 out: Oct. 18

LN 2.3, p.56; LN 2.5, p.63-66;
LN 3.2, 84-86

 Bases. Representation of elements. Number of irreducible polynomials.

7

Oct. 23-27

~

LN 2.2, p. 48-49; LN 3.2, p. 84; vzGG 14.9, p. 382-387

 Finding irreducible polynomials. Ben-Or's algorithm. Rabin's algorithm.

8

Oct. 30 - Nov. 3 

A3 in / A4 out: Nov. 1

vzGG 14.1-14.6, p. 353-373

Squarefree, distinct-degree and equal-degree factorization.

9

Nov. 6-10

~

vzGG 14.8, p. 377-382;
vzGG 14.10, p. 387-391

Berlekamp algorithm.
Cyclotomic polynomials.

10

Nov. 13-17

A4 in / A5 out: Nov. 15

LN p. 31, 89, 95-97;
vzGG p. 199-200, 391-392

 Minimal polynomials.
BCH codes revisited.

11

Nov. 20-24

~

vzGG p. 200-203

Decoding BCH codes.
Revision implementation issues.

12 

~  

~

~

Reed-Solomon Codes and
Invited talk from industry (if possible).

~

Dec. 4

A5 in: Dec. 4

~

Review of course.
Comments on final exam.

LN is ``Introduction to Finite Fields and Their Applications'', by R. Lidl and H. Niederreiter, Cambridge University Press, 1994.
vzGG is ``Modern Computer Algebra'', by J. von zur Gathen and J. Gerhard, Cambridge University Press, 1999.