Finite Fields and Coding Theory

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• The course is over.

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 2004 (before classes start).
  The actual material covered in each lecture is below.
• Textbook: There is no textbook for this course. However, for most of the lectures, we will have notes available in this webpage. They were prepared by students of a previous version of the course and checked by the professor. We may ask students to type some lectures of new material, not covered in the previous ``life'' of this course.
  We will extensively use the following book:
  • ``Introduction to Finite Fields and Their Applications'', by R. Lidl and H. Niederreiter, Cambridge University Press, 1994.
  Other books that we may use are:
  • ``Algebraic Coding Theory'', by E. Berlekamp, Aegean Park Press, 1984.
  • ``Modern Computer Algebra'', by J. von zur Gathen and J. Gerhard, Cambridge University Press, 1999.
  • ``Coding Theory and Cryptography: the Essentials'', by D.R. Hankerson, D.G Hoffman, D.A. Leonard, C.C. Lindner, K.T. Phelps, C.A. Rodger and J.R. Wall, Marcel Dekker Inc., 2000.
  • ``Finite Fields'', by R. Lidl and H. Niederreiter, Cambridge University Press, 1997.
  • ``The Theory od Error-Correcting Codes'', F.J. MacWilliams and N.J.A. Sloane, North-Holland, Elsevier Science, 1977.
  • ``Finite Fields for Computer Scientists and Engineers'', R. McEliece, Kluwer Academic Press, 1987.
• Prerequisites: MATH 2100 or 3101 or 2108 or equivalent; or permission of the School.
• Classes begin: Monday, September 13, 2004.
  Classes end: Monday, December 6, 2004.
  No lecture: Monday, October 11, 2004.
• Term mark: There will be four assignments:

  Assignment	Hand-out Date	Due Date	Contents	Worth
  1	September 29	October 20	Linear, Hamming and BCH Codes	10%
  2	October 20	November 10	Structure of Finite Fields	12.5%
  3	November 10	December 1	Polynomials; Cyclic Codes	12.5%

  You are expected to do all the assignments. No make up, early, or delayed assignments. Any missing assignments will be counted as zero.
  Total portion of the final mark in assignments: 35%. There will be a midterm test on Wednesday October 27.

• Evaluation:
  • either: term mark is 55%; final exam is 45%,
  • or: term mark is 55%; final exam is 25%; project and presentation 20%.
  Graduate students must take project and presentation option; undergraduate students may choose to have the project and presentation option. This option involves writing a brief report (15 pages) plus a presentation (25-30 minutes). 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 without academic penalties is November 05, 2004.
  
• 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 2004 (html file)
• October 2004 (html file)
• November-December 2004 (html file)

Lecture notes

• Week 1: lect1.pdf, lect2.pdf.
• Week 2: lect3.pdf; no notes for one lecture.
• Week 3: lect4.pdf, lect5.pdf.
• Week 4: lect6.pdf, lect7.pdf.
• Week 5: No lecture on October 11; brief review of the following lectures:
  lect8.pdf, lect9.pdf, lect10.pdf, lect11.pdf.
• Week 6 and 7: lect12.pdf, lect13.pdf, lect14.pdf.
• Week 8: lect15.pdf, lect16.pdf.
• Week 9: lect17.pdf; lect18.pdf.
• Week 10: lect19.pdf, lect20.pdf.
• Week 11: lect21.pdf, lect22.pdf.
• Week 12: lect23.pdf, lect24.pdf.

Contact Information: