Have an exam tomorrow. Pretty sure a question like this will be on it. Am a bit lost on this one.
Any help greatly appreciated. Thanks!
An Hamming (n,k) code is the set of all n-simbols binary word that satisfy the relation...
$\displaystyle \overline{z}= \overline {x} \cdot H= \overline {0}$ (1)
... where...
a) $\displaystyle \overline {x}$ is a n bit row vector
b) $\displaystyle \overline {z} $ is a n-k bit column vector called symdrome
c) $\displaystyle \overline {0}$ is the n-k bit 'null vector'
d) $\displaystyle H$ is the n x k bit 'parity check' matrix
An example of parity 7 x 4 Hamming parity check matrix is the following...
$\displaystyle H = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 1 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1\\ 1 & 0 & 1 \end{bmatrix}$
A 7 x 4 Hamming code can correct any single error that occurred in a 7 bits transmitted word...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$