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__Hamming Distance__
vectors in (or more generally )

__Hamming Distance__, the distance between and

__Ex__
- d(
,

- d(
,

- d(
,

- d(
,

- d(
) = 0

(Codes) is C= set of codewords

We define the __Hamming distance__ for C as

here we took so that
we did not get d(x,x)=0.
We will use hamming distance to find the codeword closest to the
decoded word and to correct an error in our encoded word. This is
called ``maximum likelihood decoding". We won't be able to to this
for the ``parity bit" codes but the ``Hamming codes" will let us
fix one error (and detect up to three) in a received word.

__Ex__ Minimum Distance for

C=

Because C is a linear code, then:

Minimum distance is 2.

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Frederick Leitner
2004-05-12