gf(2) Find null basis vectors of M

M = 00000
    00110
    10100
    10110
    11001
Augment M with identity (I) of same size
M = 00000 00001
    00110 00010
    10100 00100
    10110 01000
    11001 10000
M expressed in convenient bit depth
M = 00000000000000000000000000000001
    00000000000000000000000110000010
    00000000000000000000010100000100
    00000000000000000000010110001000
    00000000000000000000011001010000
Transform M into row reduced echelon form (rref)
M = 00000000000000000000010000001010
    00000000000000000000001001011010
    00000000000000000000000100001110
    00000000000000000000000010001100
    00000000000000000000000000000001
M in augmented form
M = 10000 01010
    01001 11010
    00100 01110
    00010 01100
    00000 00001
Highlight null basis vectors (where left side of row is zero)
M = 10000 01010
    01001 11010
    00100 01110
    00010 01100
    00000 00001
Null basis vectors

nv0 = b00000000000000000000000000000001
nv0 = 0x00000001
nv0 = 1

See also: