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 2009 (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, 2nd edition, Cambridge University Press, 2003.
  • ``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: Thursday, September 10, 2009.
  Classes end: Thursday, December 3, 2009.
  
• Term mark: There will be three 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.
  The assignments must be your own work. In particular, you must cite everything you are taking from the literature or that you discussed with someone else.
  Total portion of the final mark in assignments: 35%. There will be a midterm test on Tuesday October 27; worth of midterm test: 15%.

• Evaluation:
  • either: term mark is 50%; final exam is 50%,
  • or: term mark is 50%; final exam is 30%; 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 16, 2009.
  
• Students with Disabilities: Students with disabilities requiring academic accommodations in this course must register with the Paul Menton Centre for Students with Disabilities (PMC) for a formal evaluation of disability-related needs. Documented disabilities include but are not limited to mobility/physical impairments, specific Learning Disabilities (LD), psychiatric/psychological disabilities, sensory disabilities, Attention Deficit Hyperactivity Disorder (ADHD), and chronic medical conditions. Registered PMC students are required to contact the PMC every term to have a Letter of Accommodation sent to the Instructor by their Coordinator. In addition, students are expected to confirm their need for accommodation with the Instructor no later than two weeks before the first assignment is due or the first in-class test/midterm. If you require accommodations only for formally scheduled exam(s) in this course, you must request accommodations by the last official day to withdraw from classes in each term.

  For more general accommodation requests, see: http://www.carleton.ca/equity/accommodation/outlines.htm.

Lectures per month (summary)

• September 2009 (html file)
• October 2009 (html file)
• November-December 2009 (html file)

Lecture notes

• September lectures:
  lect1.pdf, lect2.pdf, lect3.pdf, lect4.pdf, lect5.pdf, lect6.pdf, lect7.pdf.
• Review lectures (needed material but they won't be covered in class):
  lect8.pdf, lect9.pdf, lect10.pdf, lect11.pdf.
• October lectures:
  lect12.pdf, lect13.pdf, lect14.pdf, lect15.pdf, lect16.pdf.
• November lectures:
  November3.pdf, November5.pdf,
  lect17.pdf, lect18.pdf, lect19.pdf, lect20.pdf, lect21.pdf, lect22.pdf.
• December lectures:
  lect23.pdf, lect24.pdf.

Contact Information: