mel said the following on 16/04/2007 20:01:
> Hi,
>
> Given a generator matrix G for a non systematic reed muller
> code ( first order under permutation ), how to compute the syndrome
> matrix H ?
>
>
> G = [
> 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
> 1, 0, 1, 0, 1, 0, 1, 0, 1;
> 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1,
> 1, 0, 0, 1, 1, 0, 0, 1, 1;
> 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1,
> 1, 0, 0, 0, 0, 1, 1, 1, 1;
> 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
> 0, 1, 1, 1, 1, 1, 1, 1, 1;
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1,
> 1, 1, 1, 1, 1, 1, 1, 1, 1;
> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
> 1, 1, 1, 1, 1, 1, 1, 1, 1;
> ]
>
> H = ?
>
Convert to systematic form (G => G'), then use the fact that if:
G' = [I Q]
then:
H' = [I Q^T]
Then perform the equivalent transformations (H' => H) to get back to the
original parity matrix.
--
Oli