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
    1100001100000111010010111110010
    1010111010010110110000011000011
    0111100101000110010011011111110
    1000010010101011100100100000001
    1101000111001011000000111110110
    1110010101101011111000011010011
    0011011010101000011010001000111
    1101100110100001101000100011100
    1100001000000001011001101111011
    1010011010000010011101011100111
    0100000100001100100111001101110
    0101010110110000110101101000001
    0101011101000001111111111111101
    1111110010000101010110100001101
    1011000100010000001000111000110
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
    1100001100000111010010111110010 0000000000000010000000000000000
    1010111010010110110000011000011 0000000000000100000000000000000
    0111100101000110010011011111110 0000000000001000000000000000000
    1000010010101011100100100000001 0000000000010000000000000000000
    1101000111001011000000111110110 0000000000100000000000000000000
    1110010101101011111000011010011 0000000001000000000000000000000
    0011011010101000011010001000111 0000000010000000000000000000000
    1101100110100001101000100011100 0000000100000000000000000000000
    1100001000000001011001101111011 0000001000000000000000000000000
    1010011010000010011101011100111 0000010000000000000000000000000
    0100000100001100100111001101110 0000100000000000000000000000000
    0101010110110000110101101000001 0001000000000000000000000000000
    0101011101000001111111111111101 0010000000000000000000000000000
    1111110010000101010110100001101 0100000000000000000000000000000
    1011000100010000001000111000110 1000000000000000000000000000000
M expressed in convenient bit depth
M = 0000000000000000000000000000000000000000000000000000000000000001
    0000000000000000000000000000011000000000000000000000000000000010
    0000000000000000000000000001010000000000000000000000000000000100
    0000000000000000000000000100100000000000000000000000000000001000
    0000000000000000000000010001000000000000000000000000000000010000
    0000000000000000000001000010000000000000000000000000000000100000
    0000000000000000000100000100000000000000000000000000000001000000
    0000000000000000010000001000000000000000000000000000000010000000
    0000000000000001000000010000000000000000000000000000000100000000
    0000000000000100000000100000000000000000000000000000001000000000
    0000000000010000000001000000000000000000000000000000010000000000
    0000000001000000000010000000000000000000000000000000100000000000
    0000000100000000000100000000000000000000000000000001000000000000
    0000010000000000001000000000000000000000000000000010000000000000
    0001000000000000010000000000000000000000000000000100000000000000
    0100000000000000100000000000000000000000000000001000000000000000
    0110000110000011101001011111001000000000000000010000000000000000
    0101011101001011011000001100001100000000000000100000000000000000
    0011110010100011001001101111111000000000000001000000000000000000
    0100001001010101110010010000000100000000000010000000000000000000
    0110100011100101100000011111011000000000000100000000000000000000
    0111001010110101111100001101001100000000001000000000000000000000
    0001101101010100001101000100011100000000010000000000000000000000
    0110110011010000110100010001110000000000100000000000000000000000
    0110000100000000101100110111101100000001000000000000000000000000
    0101001101000001001110101110011100000010000000000000000000000000
    0010000010000110010011100110111000000100000000000000000000000000
    0010101011011000011010110100000100001000000000000000000000000000
    0010101110100000111111111111110100010000000000000000000000000000
    0111111001000010101011010000110100100000000000000000000000000000
    0101100010001000000100011100011001000000000000000000000000000000
Transform M into row reduced echelon form (rref)
M = 0100000000000000000000000000000001111010010011001101110101101000
    0010000000000000000000000000000101110111110110111110110100011000
    0001000000000000000000000000000100101111101110111110100010110010
    0000100000000000000000000000000000001010101001100010011001000100
    0000010000000000000000000000000001100000000101111000101011100110
    0000001000000000000000000000000000101011000111111010000010101000
    0000000100000000000000000000000100100101100010000100100100010100
    0000000010000000000000000000000101101111010000000011000101111010
    0000000001000000000000000000000001100100000101100011000100101010
    0000000000100000000000000000000001101010110001000110111010001000
    0000000000010000000000000000000100101011011001110011100111011110
    0000000000001000000000000000000101001101110010101101101001011110
    0000000000000100000000000000000100101111110010111011100011000100
    0000000000000010000000000000000101010111001101100100111111010000
    0000000000000001000000000000000000010010011000000101000111001010
    0000000000000000100000000000000001111010010011000101110101101000
    0000000000000000010000000000000100101111101110111010100010110010
    0000000000000000001000000000000001100000000101111010101011100110
    0000000000000000000100000000000100100101100010000101100100010100
    0000000000000000000010000000000001100100000101100011100100101010
    0000000000000000000001000000000100101011011001110011110111011110
    0000000000000000000000100000000100101111110010111011101011000100
    0000000000000000000000010000000000010010011000000101000011001010
    0000000000000000000000001000000100101111101110111010100000110010
    0000000000000000000000000100000100100101100010000101100101010100
    0000000000000000000000000010000100101011011001110011110111111110
    0000000000000000000000000001000000010010011000000101000011011010
    0000000000000000000000000000100100100101100010000101100101011100
    0000000000000000000000000000010000010010011000000101000011011110
    0000000000000000000000000000001000010010011000000101000011011100
    0000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 1000000000000000000000000000000 1111010010011001101110101101000
    0100000000000000000000000000001 1110111110110111110110100011000
    0010000000000000000000000000001 0101111101110111110100010110010
    0001000000000000000000000000000 0001010101001100010011001000100
    0000100000000000000000000000000 1100000000101111000101011100110
    0000010000000000000000000000000 0101011000111111010000010101000
    0000001000000000000000000000001 0100101100010000100100100010100
    0000000100000000000000000000001 1101111010000000011000101111010
    0000000010000000000000000000000 1100100000101100011000100101010
    0000000001000000000000000000000 1101010110001000110111010001000
    0000000000100000000000000000001 0101011011001110011100111011110
    0000000000010000000000000000001 1001101110010101101101001011110
    0000000000001000000000000000001 0101111110010111011100011000100
    0000000000000100000000000000001 1010111001101100100111111010000
    0000000000000010000000000000000 0010010011000000101000111001010
    0000000000000001000000000000000 1111010010011000101110101101000
    0000000000000000100000000000001 0101111101110111010100010110010
    0000000000000000010000000000000 1100000000101111010101011100110
    0000000000000000001000000000001 0100101100010000101100100010100
    0000000000000000000100000000000 1100100000101100011100100101010
    0000000000000000000010000000001 0101011011001110011110111011110
    0000000000000000000001000000001 0101111110010111011101011000100
    0000000000000000000000100000000 0010010011000000101000011001010
    0000000000000000000000010000001 0101111101110111010100000110010
    0000000000000000000000001000001 0100101100010000101100101010100
    0000000000000000000000000100001 0101011011001110011110111111110
    0000000000000000000000000010000 0010010011000000101000011011010
    0000000000000000000000000001001 0100101100010000101100101011100
    0000000000000000000000000000100 0010010011000000101000011011110
    0000000000000000000000000000010 0010010011000000101000011011100
    0000000000000000000000000000000 0000000000000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 1000000000000000000000000000000 1111010010011001101110101101000
    0100000000000000000000000000001 1110111110110111110110100011000
    0010000000000000000000000000001 0101111101110111110100010110010
    0001000000000000000000000000000 0001010101001100010011001000100
    0000100000000000000000000000000 1100000000101111000101011100110
    0000010000000000000000000000000 0101011000111111010000010101000
    0000001000000000000000000000001 0100101100010000100100100010100
    0000000100000000000000000000001 1101111010000000011000101111010
    0000000010000000000000000000000 1100100000101100011000100101010
    0000000001000000000000000000000 1101010110001000110111010001000
    0000000000100000000000000000001 0101011011001110011100111011110
    0000000000010000000000000000001 1001101110010101101101001011110
    0000000000001000000000000000001 0101111110010111011100011000100
    0000000000000100000000000000001 1010111001101100100111111010000
    0000000000000010000000000000000 0010010011000000101000111001010
    0000000000000001000000000000000 1111010010011000101110101101000
    0000000000000000100000000000001 0101111101110111010100010110010
    0000000000000000010000000000000 1100000000101111010101011100110
    0000000000000000001000000000001 0100101100010000101100100010100
    0000000000000000000100000000000 1100100000101100011100100101010
    0000000000000000000010000000001 0101011011001110011110111011110
    0000000000000000000001000000001 0101111110010111011101011000100
    0000000000000000000000100000000 0010010011000000101000011001010
    0000000000000000000000010000001 0101111101110111010100000110010
    0000000000000000000000001000001 0100101100010000101100101010100
    0000000000000000000000000100001 0101011011001110011110111111110
    0000000000000000000000000010000 0010010011000000101000011011010
    0000000000000000000000000001001 0100101100010000101100101011100
    0000000000000000000000000000100 0010010011000000101000011011110
    0000000000000000000000000000010 0010010011000000101000011011100
    0000000000000000000000000000000 0000000000000000000000000000001
Null basis vectors

nv0 = b0000000000000000000000000000000000000000000000000000000000000001
nv0 = 0x0000000000000001
nv0 = 1

See also: