# M 375 Applications of Finite Fields Spring 03

## Error Correcting Codes

INSTRUCTOR: Felipe Voloch (RLM 9.122, ph.471-2674,)

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.

## Homework

1. First homework, due 02/04. In question 2, answer only the last sentence (ie compute dimension and minimal distance of the code).

2. Second homework, due 02/18. From the book. Problems 2.11, 2.12, 2.13, 3.5, 4.1, 4.2, 4.13.

3. Third homework, due 03/06. From the book. Problems 5.1, 5.2, 5.3, 5.6, 5.9, 5.11, 5.15.

4. Fourth homework, due 04/24 ( note new date). From the book. Problems 13.2, 13.3, 13.4, 13.5 and 13.6.

## Notes

While the book is unavailable, here are some rough lecture notes that might be useful: Finite fields, by D. Saltman and Error correcting codes by me.

Also available online are lecture notes by M. Sudan