Introduction to coding theory (CMU, Spr 2010)

January 15, 2010

Lecture 2 summary

Filed under: Lecture summary — Venkat Guruswami @ 3:32 pm

Today we discussed linear codes, and their representation via generator and parity check codes and their admitting systematic encodings. We extended the [7,4,3] Hamming codes to larger dimensions (and alphabets), and saw a simple syndrome decoder for correcting one error with Hamming codes. We proved the Hamming/Sphere-packing upper bound on code size as a function of distance, and saw that Hamming codes were “perfect” in that they meet this upper bound. We listed, without proof, all the binary perfect codes there are.  We defined the dual of a linear code, and then studied the distance properties of the dual of the Hamming code, the simplex code, and its extended form, the Hadamard code.

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