Posted by: atri | September 10, 2007

Lecture 6: General Hamming codes

In today’s lecture we saw two alternate characterizations of the distance of a linear code. We also defined the general Hamming code and verified that it was a perfect code.

Before the alarm went off, I was taking about the perfect binary linear codes. In fact the only possible family of such codes are:

  • Hamming code
  • (n,1,n)_2 code for odd n. (Note that the only codewords are 0^n and 1^n.
  • A (23,12)_2 code defined by Golay.

The result was proven in a sequence of work including those by van Lint and Tietavainen.

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