COURSE WEB PAGE: http://www.ma.utexas.edu/users/voloch/mathinfo4.html.
CLASS HOURS: Tue, Thu 9:30 -- 11:00 RLM 6.104
UNIQUE NUMBER: 56415
OFFICE HOURS: Wed 9:00 -- 11:00 or by appointment.
TEXTBOOK: The book is now available at the Coop. The textbook will be Algebraic codes for data transmission, by R. Blahut. Cambridge Univ. Press. I'll provide copies of chapters 1-4. We will also use the notes below.
NOTE ON PREREQUISITES: Some exposure to abstract algebra or number theory is useful but not essential. If in doubt contact instructor.
EXAMS AND GRADE POLICY: The grade will be determined from homework, a midterm and a final. Each will count 1/3 of the course grade. The midterm will be on Tuesday, March 25th during class time and the final on Friday, May 9th, 2:00 - 5:00 pm, at RLM 5.112.
COURSE DESCRIPTION:The purpose of this course is to introduce students to applications of algebra and number theory to error-correcting codes. The theory of error-correcting codes addresses the problem of preserving data integrity during transmission or storage against interference due to noise. This is essential in many aspects of modern technology: the Internet (TCP/IP), wireless communications and cellphones, CDs and DVDs, to mention a few. We hope to discuss some of the applications along with the theory.
Topics to be covered:
Introduction to finite fields, Error Correcting Codes, Vector spaces over finite fields, Hamming norm, coding, decoding. Examples of codes. Hamming, Golay, cyclic, BCH, Reed-Solomon, etc.
Also available online are lecture notes by M. Sudan