Introduction to codes from a representation-theoretic perspective
نویسنده
چکیده
1 Lecture 1: Codes and groups 2 1.1 Finite fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Matrix representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Conway polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Linear codes: generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Linear codes: examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Linear codes: automorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4.1 Application to decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
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