Introduction to Algebraic Coding Theory
نویسنده
چکیده
4 Ideals and cyclic codes 18 4.1 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Cyclic codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Group of a code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.4 Minimal polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.5 BCH and Reed-Solomon codes . . . . . . . . . . . . . . . . . . . 25 4.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
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Course Outline for CS 236610: Recent Advances in Algebraic and Combinatorial Coding Theory
The course will cover several advanced topics in algebraic and combinatorial coding theory. One of the most exciting breakthroughs in algebraic coding theory in the past decade is a new paradigm for decoding Reed-Solomon codes using bivariate (or multivariate) polynomial interpolation. The first half of the course will be devoted to an in-depth study of this subject. The second half of the cour...
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