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reed muller

Started by mel April 16, 2007
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 = ?

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