Department of Mathematics - University of Utah

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Error Correcting Codes

Jim Carlson
August 31, 1999.

Abstract. CDs and digital cell phones give remarkable audio quality, even when the CD is scratched and the air is full of radio static. The technology that makes this possible is based on the mathematics of finite fields that grew out of the work of Gauss published in 1801. The aim of the talk is to explain the technology and the mathematics which makes this possible. mathematics?

Lecture Notes. (PDF File. You'll need Adobe Acrobat Reader for this).

Courses which deal with the mathematics needed to understand error-correcting codes are Math 2270 (Linear Algebra), Math 4300 (Introduction to Algebra), Math 5010 (Introduction to Probability), Math 5310 and 5320 (Introduction to Modern Algebra I and II). You don't need to know everything in these courses to start understanding codes --- see the lecture notes above, or begin looking at the references. The book by Lindsay Childs is especially good.


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Department of Mathematics
University of Utah
155 South 1400 East, JWB 233
Salt Lake City, Utah 84112-0090
Tel: 801 581 6851, Fax: 801 581 4148
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