M 375 Applications of Finite Fields Spring 04

Error Correcting Codes


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

COURSE WEB PAGE: http://www.ma.utexas.edu/users/voloch/mathinfo5.html.

CLASS HOURS: Tue, Thu 9:30 -- 11:00 RLM 6.104


OFFICE HOURS: Wed 9:00 -- 11:00 or by appointment.

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-Muller, Reed-Solomon, etc.

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