Error Correcting Codes  

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Tentative Syllabus for Error-correcting codes SM463
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

Syllabus for Error correcting codes, SM486, Spring 2001-2

We will discuss bounds, Shannon's theorem, and examples of specific codes (Golay, LDPC, Hamming codes, ...).

Two papers due: one biography, one math paper (with at least one proof).

Computer projects: assigned MAPLE, GAP, MAGMA projects.

Homework: assigned.

Final draft of project due: April 19.
Presentations: Last week of class

Tests, quizzes: announced in class.

There will be a final exam.

Text: Applied abstract algebra notes by D. Joyner, R. Kreminski, J. Turisco

Online course notes: AAA.

Talks of interest:

  1. Feb 25, Toni Bluher, NSA
  2. April 22, David Hamer
  3. April 25, Carl Pomerance, Bell Labs
Policy statement for SM486, Spring 2001-2002
Prof. David Joyner
Office: Ch. 328
Phone: X36738, email: wdj@usna.edu
Office Hours: Wed 2nd period, F 2nd period (Math lab).

Assigned homework will be due at 6 week, 12 week, and 16 weeks. Late homework will be penalized 10 percent. Any help you receive on the homework you hand in must be clearly indicated. There are computer projects due along with the homework. They should be treated like homework. The last homework set is due the last day of class and no class work can be turned in after that. There will be a paper due which will be also presented in class. It will be due the day of the final. Grading formulas:

final grade=(.1)F+(.05)T+(.05)Q+(.2)H+(.2)CP+(.25)P+(0.05)B,

where T is the test average, Q is the quiz average, F is the final exam, H is the homework, CP is the computer projects, B is the biography, and P is the final project (.2 for the project and 0.05 for the presentation). The 6- and 12-week grades will be pro-rated.

Downloading GAP 4.3 (including share packages and all documentation) for windows: go to the web page installing gap 4.3 for windows

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