Finite Fields and Coding Theory

Current announcements

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• Lecture notes of weeks 9 and 11 are below. Lecture notes of week 10 will be ready soon.
• Assignment 5 is below.
• The final exam will be on Thursday December 7 at 2:00 pm.

General Information

• Topics: This course is an introduction to finite fields, emphasizing their structure and applications to coding theory. The influence of computational problems will be considered. Therefore, this course centers around three main issues:
  • the mathematics of finite fields,
  • the applications to coding theory, and
  • the associated computational problems.
• Tentative lecture schedule (html file) as of August 2000 (before classes start).
  The actual material covered in each lecture is below.
• Textbook: There is no textbook for this course. However, we will discuss during the first week of lectures the possibility of having in this webpage notes prepared by the students and checked by the professor.
  We will extensively use the following books:
  • ``Introduction to Finite Fields and Their Applications'', by R. Lidl and H. Niederreiter, Cambridge University Press, 1994.
  • ``Modern Computer Algebra'', by J. von zur Gathen and J. Gerhard, Cambridge University Press, 1999.
  Other books that we may use are:
  • ``Algebric Coding Theory'', by E. Berlekamp, Aegean Park Press, 1984.
  • ``Finite Fields'', by R. Lidl and H. Niederreiter, Cambridge University Press, 1997.
• Prerequisites: Mathematics 70.210 or 69.311 or 69.218 or equivalent; or permission of the School.
• Classes begin: Monday, September 11, 2000.
  Classes end: Monday, December 4, 2000.
  No lecture: Monday, October 9, 2000.
• Term mark: There will be five assignments:

  Assignment	Hand-out Date	Due Date	Contents
  1	September 18	October 4	Linear Codes
  2	October 4	October 18	2-error-correcting BCH Codes/Finite Fields
  3	October 18	November 1	Structure of Finite Fields
  4	November 1	November 15	Irreducible Polynomials and Factorization
  5	November 15	December 4	cyclic Codes

  You are expected to do all the assignments. No make up, early, or delayed assignments. Any missing assignments will be counted as zero. The average of best four assignments out of five assignments will be the term mark. Each assignment is worth 10%.

• Evaluation:
  • 70.419: term mark is 40%; final exam is 60%.
  • 70.611: term mark is 40%; final exam is 40%; project and presentation 20%.
  Graduate students project and presentation involve writing a brief report (10 pages) plus a presentation (25-30 minutes). Undergraduate students may opt to have an evaluation like the one for graduate students (project and presentation for 20% and exam for 40% instead of an exam for 60%). Here is a list of possible projects (html file). This is not a closed list of possibilities. Indeed, students interested in topics for the project and presentation that are not in this list should consult the professor about the feasibility of such a topic. Essentially, any topic related with finite fields and/or coding theory of interest to the student could be considered for the project after approval by the professor.
  
• Withdrawal: The last day for withdrawal from the course is November 03, 2000.
• Students with Disabilities: Students with Disabilities who require academic accommodations please feel free to see me, and contact the Paul Menton Centre to complete the required forms.
• Some files may be in postcript format. If you don't have a software to view postscript files, you may download a ghostview software.

Lectures per month (summary)

• September 2000 (html file)
• October 2000 (html file)
• November-December 2000 (html file)

Lecture notes

• Week 1: September 11, September 13.
• Week 2: September 18, September 20.
• Week 3: September 25, September 27.
• Week 4: October 2, October 4.
• Week 5: No lecture on October 9, October 11.
• Week 6: October 16, October 18.
• Week 7: October 23, October 25.
• Week 8: November 1, November 3.
• Week 9: November 6, November 8.
• Week 11: November 20, November 22.

Assignments

• Assignment 1 (postcript form).
• Assignment 2 (postcript form).
• Assignment 3 (postcript form).
• Assignment 4 (postcript form).
• Assignment 5 (postcript form).

Contact Information: