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MATH 295 Error-Correcting Codes 6 credits
This course explores the mathematics behind error-correcting codes – the science of transmitting information reliably over noisy channels. How can a message be recovered after it has been corrupted in transit? How much redundancy must be introduced to guarantee accurate transmission? A "code" here refers to a carefully designed set of codewords, strings of symbols built to withstand errors. Codes of this kind are everywhere: they underpin QR codes, ISBN numbers, and solid-state drives. We begin with the fundamental ideas of error detection and correction before developing the theory of linear codes, the central objects of study, with examples including Hamming, Golay, and Reed-Muller codes. The course is proof-based, and all necessary background in finite fields and linear algebra is developed within the course.
Repeatable: Course is repeatable provided the topics are different.
- Winter 2027
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 with a grade of C- or better or received a Carleton Mathematics 236 Requisite Equivalency.