Finite Fields and Coding Theory

Current announcements

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• The final marks are available in HP4372.
• Read Tony Rothman's excellent article (available at http://godel.ph.utexas.edu/~tonyr/galois.html) about Galois! (postcript format).

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 2002 (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: Mathematics 70.210 or 69.311 or 69.218 or equivalent; or permission of the School.
• Classes begin: Monday, September 9, 2002.
  Classes end: Monday, December 2, 2002.
  No lecture: Monday, October 14, 2002.
• Term mark: There will be four assignments:

  Assignment	Hand-out Date	Due Date	Contents	Worth
  1	September 25	October 16	Linear and Hamming Codes	12.5%
  2	October 16	October 30	2-error-correcting BCH Codes; Finite Fields	12.5%
  3	October 30	November 18	Structure of Finite Fields; Irreducible Polynomials	12.5%
  4	November 18	December 4	Factorization; Cyclic Codes; Minimal polynomials	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: 50%.

• Evaluation:
  • 70.419: term mark is 50%; final exam is 50%.
  • 70.611: term mark is 50%; final exam is 25%; project and presentation 25%.
  Graduate students project and presentation involve writing a brief report (15 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 25% and exam for 25% instead of an exam for 50%). 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 01, 2002.
  The last day for withdrawal from the course receiving back the full fee paid is September 30, 2002.
• 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 2002 (html file)
• October 2002 (html file)
• November-December 2002 (html file)

Lecture notes

• Week 1: lect1.ps, lect2.ps.
• Week 2: lect3.ps, lect4.ps.
• Week 3: lect5.pdf, lect6.pdf.
• Week 4: lect7.pdf ; brief review of the following lectures:
  lect8.pdf, lect9.pdf, lect10.pdf, lect11.pdf.
• Week 5: lect12.pdf, lect13.pdf.
• Week 6: No lecture on October 14; lect14.pdf.
• Week 7: lect15.pdf, lect16.pdf.
• Week 8: lect17.pdf; notes.
• Week 9: lect18.pdf, lect19.pdf.
• Week 10: lect20.pdf.
• Week 11: lect21.pdf, lect22.pdf.
• Week 12: lect23.pdf, lect24.pdf.

Contact Information: