# Error Correcting Codes

**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**:

- Weekly homework,
- Paper due: Term paper (with at least one proof or description of algorithm) on approved topic.
- MAPLE project,
- GAP coding theory exercises,

Rough draft of project due: Nov 11

Second draft due: Nov 30

Final draft due: day of final exam.

Tests and quizzes: as announced.

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.

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

Talks of interest:

**Policy statement for SM486, Spring 2001-2002**

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:

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 (including share packages and all documentation) for windows: go to this web page.