Tentative Syllabus for Error-correcting codes
Fall 2005-2006
Text: Raymond Hill, A first course in coding theory, Oxford Univ Press, 1986.

Class schedule:

chapter
 topics
 exercises
1
 introduction
 1.2-1.5
2
 maximum size of "good" code?
 2.1-2.4, 2.6-2.12, 2.17-2.19
3 finite fields, introduction
 all
4 vector spaces over finite fields
 4.1-4.6
5 linear codes, introduction
 5.1-5.7, 5.10, 5.11
6 encoding, decoding
 6.1, 6.2, 6.4,. 6.5, 6.7-6.9
7 dual code, check matrix, syndrome decoding
 all
8 Hamming codes
 8.1-8.10,  8.11(a)
12 Cyclic codes
 12.1-12.22
13 Weight enumerators
 13.1-13.13(a)

Hopefully there will be some time at the end to discuss chapter 14 and for student presentations.

Assignments:
  1. Weekly homework,
  2. Paper due: Term paper (with at least one proof or description of algorithm) on approved topic.
  3. MAPLE project: MAPLE coding theory exercises
  4. GAP coding theory exercises (a tutorial on some basics of GAP),
Rough draft of project due: Nov 11
Second draft due: Nov 30
Final draft due: day of final exam.

Tests and quizzes: as announced.

Policy statement
A selection of some term papers in pdf:

Latin squares and codes by J. Thibault and E. Crownover
Golay codes by K. Clark and T. marley
McEliese's cryptosystem by C. McFarlane and Y. Sauls
LFSRs and the Berlekamp-Massey algorithm by T. Brock and R. Rivas

David Joyner 12-31-2003, last modified 12-19-2005