gf(2) Find null basis vectors of M

M = 000000000000000000000
    000000000000000000110
    000000000000000010100
    000000000000001001000
    000000000000100010000
    000000000010000100000
    000000001000001000000
    000000100000010000000
    000010000000100000000
    001000000001000000000
    100000000010000000000
    011110001110100110010
    110111100111001010001
    001111100011011101111
    111111101101110111100
    101100111000101011011
    101011101000001011110
    111100101010001001010
    111011100111010000011
    001111010010110100111
    010010001110000000101
Augment M with identity (I) of same size
M = 000000000000000000000 000000000000000000001
    000000000000000000110 000000000000000000010
    000000000000000010100 000000000000000000100
    000000000000001001000 000000000000000001000
    000000000000100010000 000000000000000010000
    000000000010000100000 000000000000000100000
    000000001000001000000 000000000000001000000
    000000100000010000000 000000000000010000000
    000010000000100000000 000000000000100000000
    001000000001000000000 000000000001000000000
    100000000010000000000 000000000010000000000
    011110001110100110010 000000000100000000000
    110111100111001010001 000000001000000000000
    001111100011011101111 000000010000000000000
    111111101101110111100 000000100000000000000
    101100111000101011011 000001000000000000000
    101011101000001011110 000010000000000000000
    111100101010001001010 000100000000000000000
    111011100111010000011 001000000000000000000
    001111010010110100111 010000000000000000000
    010010001110000000101 100000000000000000000
M expressed in convenient bit depth
M = 0000000000000000000000000000000000000000000000000000000000000001
    0000000000000000000000000000000000000001100000000000000000000010
    0000000000000000000000000000000000000101000000000000000000000100
    0000000000000000000000000000000000010010000000000000000000001000
    0000000000000000000000000000000001000100000000000000000000010000
    0000000000000000000000000000000100001000000000000000000000100000
    0000000000000000000000000000010000010000000000000000000001000000
    0000000000000000000000000001000000100000000000000000000010000000
    0000000000000000000000000100000001000000000000000000000100000000
    0000000000000000000000010000000010000000000000000000001000000000
    0000000000000000000001000000000100000000000000000000010000000000
    0000000000000000000000111100011101001100100000000000100000000000
    0000000000000000000001101111001110010100010000000001000000000000
    0000000000000000000000011111000110111011110000000010000000000000
    0000000000000000000001111111011011101111000000000100000000000000
    0000000000000000000001011001110001010110110000001000000000000000
    0000000000000000000001010111010000010111100000010000000000000000
    0000000000000000000001111001010100010010100000100000000000000000
    0000000000000000000001110111001110100000110001000000000000000000
    0000000000000000000000011110100101101001110010000000000000000000
    0000000000000000000000100100011100000001010100000000000000000000
Transform M into row reduced echelon form (rref)
M = 0000000000000000000001000000000000000000010110011011000101011000
    0000000000000000000000100000000000000000000110101001011111110110
    0000000000000000000000010000000000000000010011011111110100010000
    0000000000000000000000001000000000000000010001000100000001111010
    0000000000000000000000000100000000000000000111001000001000101110
    0000000000000000000000000010000000000000000110001110000011111110
    0000000000000000000000000001000000000000010110001111111010001000
    0000000000000000000000000000100000000000000000011010001010111110
    0000000000000000000000000000010000000000010101010101001100100100
    0000000000000000000000000000001000000000010001100111000010011110
    0000000000000000000000000000000100000000010110011011010101011000
    0000000000000000000000000000000010000000010011011111111100010000
    0000000000000000000000000000000001000000000111001000001100101110
    0000000000000000000000000000000000100000010110001111111000001000
    0000000000000000000000000000000000010000010101010101001101100100
    0000000000000000000000000000000000001000010110011011010101111000
    0000000000000000000000000000000000000100000111001000001100111110
    0000000000000000000000000000000000000010010101010101001101101100
    0000000000000000000000000000000000000001000111001000001100111010
    0000000000000000000000000000000000000000100111001000001100111000
    0000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 100000000000000000001 110011011000101011000
    010000000000000000000 110101001011111110110
    001000000000000000001 011011111110100010000
    000100000000000000001 001000100000001111010
    000010000000000000000 111001000001000101110
    000001000000000000000 110001110000011111110
    000000100000000000001 110001111111010001000
    000000010000000000000 000011010001010111110
    000000001000000000001 101010101001100100100
    000000000100000000001 001100111000010011110
    000000000010000000001 110011011010101011000
    000000000001000000001 011011111111100010000
    000000000000100000000 111001000001100101110
    000000000000010000001 110001111111000001000
    000000000000001000001 101010101001101100100
    000000000000000100001 110011011010101111000
    000000000000000010000 111001000001100111110
    000000000000000001001 101010101001101101100
    000000000000000000100 111001000001100111010
    000000000000000000010 111001000001100111000
    000000000000000000000 000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 100000000000000000001 110011011000101011000
    010000000000000000000 110101001011111110110
    001000000000000000001 011011111110100010000
    000100000000000000001 001000100000001111010
    000010000000000000000 111001000001000101110
    000001000000000000000 110001110000011111110
    000000100000000000001 110001111111010001000
    000000010000000000000 000011010001010111110
    000000001000000000001 101010101001100100100
    000000000100000000001 001100111000010011110
    000000000010000000001 110011011010101011000
    000000000001000000001 011011111111100010000
    000000000000100000000 111001000001100101110
    000000000000010000001 110001111111000001000
    000000000000001000001 101010101001101100100
    000000000000000100001 110011011010101111000
    000000000000000010000 111001000001100111110
    000000000000000001001 101010101001101101100
    000000000000000000100 111001000001100111010
    000000000000000000010 111001000001100111000
    000000000000000000000 000000000000000000001
Null basis vectors

nv0 = b0000000000000000000000000000000000000000000000000000000000000001
nv0 = 0x0000000000000001
nv0 = 1

See also: