Claremont McKenna College, Fall 2016
MATH 195: Coding Theory
Instructor:
Time:
Lenny Fukshansky, Adams Hall 218, (909) 607 - 0014, [email protected]
Tuesdays and Thursdays, 2:45 – 4:00 pm
Prerequisite: MATH 60 or instructor’s consent. I am happy to talk to anybody interested
in this course, and in particular to discuss if their background is sufficient.
Course Description: The Theory of Error-Correcting Codes is an exciting branch of
Mathematics at the intersection with Computer Science and Information Theory. It
addresses one of the basic problems of Information Theory: assuming data transmission
over a potentially noisy channel, how to insure self-correction of errors upon receipt with
good probability while keeping the transmission speed high? A solution to this problem
requires machinery from Linear and Abstract Algebra, as well as Number Theory.
The goal of this course is to demonstrate some mathematical ideas behind the design of
error-correcting codes. We will introduce the subject in terms of an optimization problem
involving the famous Hamming distance and develop the basic theory of linear codes as
vector spaces over finite fields and associated polynomial rings. Some additional topics
may include codes from lattices and algebraic curves, spherical codes, and connections to
packing and covering problems, as time allows. The only prerequisite for this course is
knowledge of linear algebra.
Grading: Based on some combination of homework assignments, a midterm, and a final.
Registration is open to students from all of the Claremont Colleges, and I am happy
to talk to anyone interested in this course!