## Math 626- Coding Theory Schedule and Assignments

Here is a revision (3/19) of John Cook's quick and easy finite field material.
Here is my Maple Worksheet on finite fields.

that I taught with Joe Mahaffy.
Try parts of the first lesson to get started. Then my lessons, #7 and #10.

### Schedule

I will try to keep to this schedule but will update it as needed.
Day Topics Preparation
Wed. 1/23 Introduction. .
Mon. 1/28 Review of number theory Notes Sec 3.
Wed 1/30 Polynomials over a field. Finite fields. Notes Sec. 4.
Mon. 2/4 Structure of Finite Fields Sec. 4, 5.
Wed. 2/6 Still more on finite fields,
the Euclidean algorithm, matrix version, Maple
.
Mon. 2/11 Coding for error correction.
Reed-Solomon codes
.
Wed. 2/13 Maple, meet in BAM 120 .
Mon. 2/18 Encoding of RS codes.
Cyclic codes
.
Wed. 2/20 Ideals .
Mon. 2/25 ? .
Wed. 2/27 Decoding, the syndrome map .
Mon. 3/4 The Berlekamp-Massey algorithm .
Wed. 3/6 The syndrome polynomial and evaluator polynomial .
Mon. 3/11 Extended BM algorithm.
An alternative method for error evaluation
.
Wed. 3/13 Berlekamp-Massey with computation of error evaluator polynomial.
A better error evaluation formula
.
Mon. 3/18 Probability, Bayes' theorem and decoding .
Wed. 3/20 Channels, a decoding example .
Mon. 3/25 The generalised distributive law
decoding on trees
.
Wed. 3/27 no class .
Mon. 4/8 Local algorithms approximating the GDL .
Wed. 4/10 Implementation of iterative decoding .
Mon. 4/15 Majority logic decoding, erasure decoding
Construction of LDPC codes
Luby, Mitzenmacher, et al.
Wed. 4/17 Steve Hui and Jim Bond on constructions .
Mon. 4/22 Constructions using groups Margullis, Rosenthal-Vontobel.
Wed. 4/24 More on Hui/Bond techniques
using linear congruences
.
Mon. 4/29 Meet in lab, show me your work,
I'll give you more
.
Wed. 5/1 Using geometry to create a parity check code Fossorier et al
Mon. 5/6 Meet in lab, show me your work,
I'll give you more
.
Wed. 5/8 cancelled .

### Assignments

Due dates may change depending on schedule.
Due date Section Problems
Wed. 2/6 5 1-4
Mon. 3/11 See notes .
Wed. 3/20 See notes .
Mon. 4/22 Exercise list 1-5