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RREF to make the generator matrix in the form G= [ Parity | Identity ] 



RREF : 1. Leading elements move to the right. 2. Leading elements are the only nonzero elements in their columns and Equal 1. 3. Zero rows at the bottom. Example : 1 1 1 0 0 Given G= 0 0 1 1 0 Change the 2nd by the 3rd row 1 1 1 1 1 1 G= 1 0

1 1 0 0 1 1 1 1 0 1 1 0

xor the 1st with the 2nd row

1 G= 0 0

1 1 0 0 0 0 1 1 0 1 1 0

xor the 3rd with the 2nd row

1 G= 0 0

1 1 0 0 0 1 0 1 0 1 1 0

xor the 2nd with the 1st row

1 G= 0 0

1 0 0 1 0 1 0 1 0 1 1 0

xor the 2nd with the 3rd row

1 G= 0 0

1 0 0 1 0 1 0 1 0 0 1 1

just arrange the rows to be G= [ P | I ]

đ?&#x;? đ?&#x;? G= đ?&#x;Ž đ?&#x;? đ?&#x;Ž đ?&#x;?

đ?&#x;? đ?&#x;Ž đ?&#x;Ž

đ?&#x;Ž đ?&#x;? đ?&#x;Ž

đ?&#x;Ž đ?&#x;Ž đ?&#x;?

Abd ALLAH.Moetaz bellah


RREF for a generator matrix  

The example from the last lecture

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