gf(2) Find null basis vectors of M

M = 00000
    00110
    10100
    10001
    11010
Augment M with identity (I) of same size
M = 00000 00001
    00110 00010
    10100 00100
    10001 01000
    11010 10000
M expressed in convenient bit depth
M = 00000000000000000000000000000001
    00000000000000000000000110000010
    00000000000000000000010100000100
    00000000000000000000010001001000
    00000000000000000000011010010000
Transform M into row reduced echelon form (rref)
M = 00000000000000000000010001001000
    00000000000000000000001000010110
    00000000000000000000000101001100
    00000000000000000000000011001110
    00000000000000000000000000000001
M in augmented form
M = 10001 01000
    01000 10110
    00101 01100
    00011 01110
    00000 00001
Highlight null basis vectors (where left side of row is zero)
M = 10001 01000
    01000 10110
    00101 01100
    00011 01110
    00000 00001
Null basis vectors

nv0 = b00000000000000000000000000000001
nv0 = 0x00000001
nv0 = 1

See also: