gf(2) Find null basis vectors of M

M = 0000000000000000000000000000000
    0000000000000000000000000000110
    0000000000000000000000000010100
    0000000000000000000000001001000
    0000000000000000000000100010000
    0000000000000000000010000100000
    0000000000000000001000001000000
    0000000000000000100000010000000
    0000000000000010000000100000000
    0000000000001000000001000000000
    0000000000100000000010000000000
    0000000010000000000100000000000
    0000001000000000001000000000000
    0000100000000000010000000000000
    0010000000000000100000000000000
    1000000000000001000000000000000
    0111100000101101000010100100001
    0011011101011101001011110011011
    1101110101101100101111001101100
    1101101001001000111111110001110
    1100011010001001111100000000110
    1011010100101101110011000100110
    1010110100011000001110110111001
    1100111101001111111001111000101
    1001010011110101100100100101010
    0010011111111001010000110001001
    1000011111100101000011000100100
    0101011110111011001110110110001
    1110100100001001111010111011011
    1100101111101101101000101010010
    1101011110011001100000001101001
Augment M with identity (I) of same size
M = 0000000000000000000000000000000 0000000000000000000000000000001
    0000000000000000000000000000110 0000000000000000000000000000010
    0000000000000000000000000010100 0000000000000000000000000000100
    0000000000000000000000001001000 0000000000000000000000000001000
    0000000000000000000000100010000 0000000000000000000000000010000
    0000000000000000000010000100000 0000000000000000000000000100000
    0000000000000000001000001000000 0000000000000000000000001000000
    0000000000000000100000010000000 0000000000000000000000010000000
    0000000000000010000000100000000 0000000000000000000000100000000
    0000000000001000000001000000000 0000000000000000000001000000000
    0000000000100000000010000000000 0000000000000000000010000000000
    0000000010000000000100000000000 0000000000000000000100000000000
    0000001000000000001000000000000 0000000000000000001000000000000
    0000100000000000010000000000000 0000000000000000010000000000000
    0010000000000000100000000000000 0000000000000000100000000000000
    1000000000000001000000000000000 0000000000000001000000000000000
    0111100000101101000010100100001 0000000000000010000000000000000
    0011011101011101001011110011011 0000000000000100000000000000000
    1101110101101100101111001101100 0000000000001000000000000000000
    1101101001001000111111110001110 0000000000010000000000000000000
    1100011010001001111100000000110 0000000000100000000000000000000
    1011010100101101110011000100110 0000000001000000000000000000000
    1010110100011000001110110111001 0000000010000000000000000000000
    1100111101001111111001111000101 0000000100000000000000000000000
    1001010011110101100100100101010 0000001000000000000000000000000
    0010011111111001010000110001001 0000010000000000000000000000000
    1000011111100101000011000100100 0000100000000000000000000000000
    0101011110111011001110110110001 0001000000000000000000000000000
    1110100100001001111010111011011 0010000000000000000000000000000
    1100101111101101101000101010010 0100000000000000000000000000000
    1101011110011001100000001101001 1000000000000000000000000000000
M expressed in convenient bit depth
M = 0000000000000000000000000000000000000000000000000000000000000001
    0000000000000000000000000000011000000000000000000000000000000010
    0000000000000000000000000001010000000000000000000000000000000100
    0000000000000000000000000100100000000000000000000000000000001000
    0000000000000000000000010001000000000000000000000000000000010000
    0000000000000000000001000010000000000000000000000000000000100000
    0000000000000000000100000100000000000000000000000000000001000000
    0000000000000000010000001000000000000000000000000000000010000000
    0000000000000001000000010000000000000000000000000000000100000000
    0000000000000100000000100000000000000000000000000000001000000000
    0000000000010000000001000000000000000000000000000000010000000000
    0000000001000000000010000000000000000000000000000000100000000000
    0000000100000000000100000000000000000000000000000001000000000000
    0000010000000000001000000000000000000000000000000010000000000000
    0001000000000000010000000000000000000000000000000100000000000000
    0100000000000000100000000000000000000000000000001000000000000000
    0011110000010110100001010010000100000000000000010000000000000000
    0001101110101110100101111001101100000000000000100000000000000000
    0110111010110110010111100110110000000000000001000000000000000000
    0110110100100100011111111000111000000000000010000000000000000000
    0110001101000100111110000000011000000000000100000000000000000000
    0101101010010110111001100010011000000000001000000000000000000000
    0101011010001100000111011011100100000000010000000000000000000000
    0110011110100111111100111100010100000000100000000000000000000000
    0100101001111010110010010010101000000001000000000000000000000000
    0001001111111100101000011000100100000010000000000000000000000000
    0100001111110010100001100010010000000100000000000000000000000000
    0010101111011101100111011011000100001000000000000000000000000000
    0111010010000100111101011101101100010000000000000000000000000000
    0110010111110110110100010101001000100000000000000000000000000000
    0110101111001100110000000110100101000000000000000000000000000000
Transform M into row reduced echelon form (rref)
M = 0100000000000000000000000000000100110110111011011111101111101100
    0010000000000000000000000000000100111110010011100010010101000100
    0001000000000000000000000000000000101001101010001010101010110100
    0000100000000000000000000000000001110100011000010001100000101110
    0000010000000000000000000000000001110101011111100000111001001010
    0000001000000000000000000000000101000110100110001100001111001000
    0000000100000000000000000000000000111101101100011100101011100110
    0000000010000000000000000000000101000011110001011101100110101110
    0000000001000000000000000000000001000011001110111001101010011010
    0000000000100000000000000000000101011111110000100010101001110110
    0000000000010000000000000000000001011101111001010010010001001110
    0000000000001000000000000000000000100001101001011000011111010010
    0000000000000100000000000000000000100100000100001011101001110000
    0000000000000010000000000000000001011001100001111100101001101110
    0000000000000001000000000000000100000000011001111011011100001000
    0000000000000000100000000000000100110110111011010111101111101100
    0000000000000000010000000000000000101001101010001110101010110100
    0000000000000000001000000000000001110101011111100010111001001010
    0000000000000000000100000000000000111101101100011101101011100110
    0000000000000000000010000000000001000011001110111001001010011010
    0000000000000000000001000000000001011101111001010010000001001110
    0000000000000000000000100000000000100100000100001011100001110000
    0000000000000000000000010000000100000000011001111011011000001000
    0000000000000000000000001000000000101001101010001110101000110100
    0000000000000000000000000100000000111101101100011101101010100110
    0000000000000000000000000010000001011101111001010010000001101110
    0000000000000000000000000001000100000000011001111011011000011000
    0000000000000000000000000000100000111101101100011101101010101110
    0000000000000000000000000000010100000000011001111011011000011100
    0000000000000000000000000000001100000000011001111011011000011110
    0000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 1000000000000000000000000000001 0110110111011011111101111101100
    0100000000000000000000000000001 0111110010011100010010101000100
    0010000000000000000000000000000 0101001101010001010101010110100
    0001000000000000000000000000000 1110100011000010001100000101110
    0000100000000000000000000000000 1110101011111100000111001001010
    0000010000000000000000000000001 1000110100110001100001111001000
    0000001000000000000000000000000 0111101101100011100101011100110
    0000000100000000000000000000001 1000011110001011101100110101110
    0000000010000000000000000000000 1000011001110111001101010011010
    0000000001000000000000000000001 1011111110000100010101001110110
    0000000000100000000000000000000 1011101111001010010010001001110
    0000000000010000000000000000000 0100001101001011000011111010010
    0000000000001000000000000000000 0100100000100001011101001110000
    0000000000000100000000000000000 1011001100001111100101001101110
    0000000000000010000000000000001 0000000011001111011011100001000
    0000000000000001000000000000001 0110110111011010111101111101100
    0000000000000000100000000000000 0101001101010001110101010110100
    0000000000000000010000000000000 1110101011111100010111001001010
    0000000000000000001000000000000 0111101101100011101101011100110
    0000000000000000000100000000000 1000011001110111001001010011010
    0000000000000000000010000000000 1011101111001010010000001001110
    0000000000000000000001000000000 0100100000100001011100001110000
    0000000000000000000000100000001 0000000011001111011011000001000
    0000000000000000000000010000000 0101001101010001110101000110100
    0000000000000000000000001000000 0111101101100011101101010100110
    0000000000000000000000000100000 1011101111001010010000001101110
    0000000000000000000000000010001 0000000011001111011011000011000
    0000000000000000000000000001000 0111101101100011101101010101110
    0000000000000000000000000000101 0000000011001111011011000011100
    0000000000000000000000000000011 0000000011001111011011000011110
    0000000000000000000000000000000 0000000000000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 1000000000000000000000000000001 0110110111011011111101111101100
    0100000000000000000000000000001 0111110010011100010010101000100
    0010000000000000000000000000000 0101001101010001010101010110100
    0001000000000000000000000000000 1110100011000010001100000101110
    0000100000000000000000000000000 1110101011111100000111001001010
    0000010000000000000000000000001 1000110100110001100001111001000
    0000001000000000000000000000000 0111101101100011100101011100110
    0000000100000000000000000000001 1000011110001011101100110101110
    0000000010000000000000000000000 1000011001110111001101010011010
    0000000001000000000000000000001 1011111110000100010101001110110
    0000000000100000000000000000000 1011101111001010010010001001110
    0000000000010000000000000000000 0100001101001011000011111010010
    0000000000001000000000000000000 0100100000100001011101001110000
    0000000000000100000000000000000 1011001100001111100101001101110
    0000000000000010000000000000001 0000000011001111011011100001000
    0000000000000001000000000000001 0110110111011010111101111101100
    0000000000000000100000000000000 0101001101010001110101010110100
    0000000000000000010000000000000 1110101011111100010111001001010
    0000000000000000001000000000000 0111101101100011101101011100110
    0000000000000000000100000000000 1000011001110111001001010011010
    0000000000000000000010000000000 1011101111001010010000001001110
    0000000000000000000001000000000 0100100000100001011100001110000
    0000000000000000000000100000001 0000000011001111011011000001000
    0000000000000000000000010000000 0101001101010001110101000110100
    0000000000000000000000001000000 0111101101100011101101010100110
    0000000000000000000000000100000 1011101111001010010000001101110
    0000000000000000000000000010001 0000000011001111011011000011000
    0000000000000000000000000001000 0111101101100011101101010101110
    0000000000000000000000000000101 0000000011001111011011000011100
    0000000000000000000000000000011 0000000011001111011011000011110
    0000000000000000000000000000000 0000000000000000000000000000001
Null basis vectors

nv0 = b0000000000000000000000000000000000000000000000000000000000000001
nv0 = 0x0000000000000001
nv0 = 1

See also: