gf(2) Find null basis vectors of M

M = 00000000000000000000000000000000000000000000000
    00000000000000000000000000000000000000000000110
    00000000000000000000000000000000000000000010100
    00000000000000000000000000000000000000001001000
    00000000000000000000000000000000000000100010000
    00000000000000000000000000000000000010000100000
    00000000000000000000000000000000001000001000000
    00000000000000000000000000000000100000010000000
    00000000000000000000000000000010000000100000000
    00000000000000000000000000001000000001000000000
    00000000000000000000000000100000000010000000000
    00000000000000000000000010000000000100000000000
    00000000000000000000001000000000001000000000000
    00000000000000000000100000000000010000000000000
    00000000000000000010000000000000100000000000000
    00000000000000001000000000000001000000000000000
    00000000000000100000000000000010000000000000000
    00000000000010000000000000000100000000000000000
    00000000001000000000000000001000000000000000000
    00000000100000000000000000010000000000000000000
    00000010000000000000000000100000000000000000000
    00001000000000000000000001000000000000000000000
    00100000000000000000000010000000000000000000000
    10000000000000000000000100000000000000000000000
    00110000110101101101100101000000001010101000001
    11000011010110110110100100000000101010100000100
    11010010000010010010111001111101011001001101110
    10010111010000000001101110001010010111111000110
    01101101110101101101010101101001010101001011001
    01011000111010011101110010011010101101001011011
    10001100000101001011101101010101001101001010011
    00000000100001110011011000010100111110000001101
    00000010000110101101100001010011111000000110100
    00001000011001110110000101001111100000011010000
    00100001100001011000010100111110000001101000000
    10000110001001100001010011111000000110100000000
    00101000001011101000100010100000010000101000001
    10100000011110100010001010000001000010100000100
    10110000101111100101000101000100000000101010001
    11110001001011111001111001010000001000000000101
    00011101110110101110101100111111010011001101010
    01111011011010111010110011111101001100110101000
    00011010000111001111101011001011001010110011111
    01011000011100111110101100101100101011001111100
    11101110011111011110010110001101010101011001111
    10100110100100110000010001001010100110101000010
    11000101001010001000001101010101101001101110110
Augment M with identity (I) of same size
M = 00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000001
    00000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000010100 00000000000000000000000000000000000000000000100
    00000000000000000000000000000000000000001001000 00000000000000000000000000000000000000000001000
    00000000000000000000000000000000000000100010000 00000000000000000000000000000000000000000010000
    00000000000000000000000000000000000010000100000 00000000000000000000000000000000000000000100000
    00000000000000000000000000000000001000001000000 00000000000000000000000000000000000000001000000
    00000000000000000000000000000000100000010000000 00000000000000000000000000000000000000010000000
    00000000000000000000000000000010000000100000000 00000000000000000000000000000000000000100000000
    00000000000000000000000000001000000001000000000 00000000000000000000000000000000000001000000000
    00000000000000000000000000100000000010000000000 00000000000000000000000000000000000010000000000
    00000000000000000000000010000000000100000000000 00000000000000000000000000000000000100000000000
    00000000000000000000001000000000001000000000000 00000000000000000000000000000000001000000000000
    00000000000000000000100000000000010000000000000 00000000000000000000000000000000010000000000000
    00000000000000000010000000000000100000000000000 00000000000000000000000000000000100000000000000
    00000000000000001000000000000001000000000000000 00000000000000000000000000000001000000000000000
    00000000000000100000000000000010000000000000000 00000000000000000000000000000010000000000000000
    00000000000010000000000000000100000000000000000 00000000000000000000000000000100000000000000000
    00000000001000000000000000001000000000000000000 00000000000000000000000000001000000000000000000
    00000000100000000000000000010000000000000000000 00000000000000000000000000010000000000000000000
    00000010000000000000000000100000000000000000000 00000000000000000000000000100000000000000000000
    00001000000000000000000001000000000000000000000 00000000000000000000000001000000000000000000000
    00100000000000000000000010000000000000000000000 00000000000000000000000010000000000000000000000
    10000000000000000000000100000000000000000000000 00000000000000000000000100000000000000000000000
    00110000110101101101100101000000001010101000001 00000000000000000000001000000000000000000000000
    11000011010110110110100100000000101010100000100 00000000000000000000010000000000000000000000000
    11010010000010010010111001111101011001001101110 00000000000000000000100000000000000000000000000
    10010111010000000001101110001010010111111000110 00000000000000000001000000000000000000000000000
    01101101110101101101010101101001010101001011001 00000000000000000010000000000000000000000000000
    01011000111010011101110010011010101101001011011 00000000000000000100000000000000000000000000000
    10001100000101001011101101010101001101001010011 00000000000000001000000000000000000000000000000
    00000000100001110011011000010100111110000001101 00000000000000010000000000000000000000000000000
    00000010000110101101100001010011111000000110100 00000000000000100000000000000000000000000000000
    00001000011001110110000101001111100000011010000 00000000000001000000000000000000000000000000000
    00100001100001011000010100111110000001101000000 00000000000010000000000000000000000000000000000
    10000110001001100001010011111000000110100000000 00000000000100000000000000000000000000000000000
    00101000001011101000100010100000010000101000001 00000000001000000000000000000000000000000000000
    10100000011110100010001010000001000010100000100 00000000010000000000000000000000000000000000000
    10110000101111100101000101000100000000101010001 00000000100000000000000000000000000000000000000
    11110001001011111001111001010000001000000000101 00000001000000000000000000000000000000000000000
    00011101110110101110101100111111010011001101010 00000010000000000000000000000000000000000000000
    01111011011010111010110011111101001100110101000 00000100000000000000000000000000000000000000000
    00011010000111001111101011001011001010110011111 00001000000000000000000000000000000000000000000
    01011000011100111110101100101100101011001111100 00010000000000000000000000000000000000000000000
    11101110011111011110010110001101010101011001111 00100000000000000000000000000000000000000000000
    10100110100100110000010001001010100110101000010 01000000000000000000000000000000000000000000000
    11000101001010001000001101010101101001101110110 10000000000000000000000000000000000000000000000
M expressed in convenient bit depth
M = 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
    000000000000000000000000000000000000000000000110000000000000000000000000000000000000000000000010
    000000000000000000000000000000000000000000010100000000000000000000000000000000000000000000000100
    000000000000000000000000000000000000000001001000000000000000000000000000000000000000000000001000
    000000000000000000000000000000000000000100010000000000000000000000000000000000000000000000010000
    000000000000000000000000000000000000010000100000000000000000000000000000000000000000000000100000
    000000000000000000000000000000000001000001000000000000000000000000000000000000000000000001000000
    000000000000000000000000000000000100000010000000000000000000000000000000000000000000000010000000
    000000000000000000000000000000010000000100000000000000000000000000000000000000000000000100000000
    000000000000000000000000000001000000001000000000000000000000000000000000000000000000001000000000
    000000000000000000000000000100000000010000000000000000000000000000000000000000000000010000000000
    000000000000000000000000010000000000100000000000000000000000000000000000000000000000100000000000
    000000000000000000000001000000000001000000000000000000000000000000000000000000000001000000000000
    000000000000000000000100000000000010000000000000000000000000000000000000000000000010000000000000
    000000000000000000010000000000000100000000000000000000000000000000000000000000000100000000000000
    000000000000000001000000000000001000000000000000000000000000000000000000000000001000000000000000
    000000000000000100000000000000010000000000000000000000000000000000000000000000010000000000000000
    000000000000010000000000000000100000000000000000000000000000000000000000000000100000000000000000
    000000000001000000000000000001000000000000000000000000000000000000000000000001000000000000000000
    000000000100000000000000000010000000000000000000000000000000000000000000000010000000000000000000
    000000010000000000000000000100000000000000000000000000000000000000000000000100000000000000000000
    000001000000000000000000001000000000000000000000000000000000000000000000001000000000000000000000
    000100000000000000000000010000000000000000000000000000000000000000000000010000000000000000000000
    010000000000000000000000100000000000000000000000000000000000000000000000100000000000000000000000
    000110000110101101101100101000000001010101000001000000000000000000000001000000000000000000000000
    011000011010110110110100100000000101010100000100000000000000000000000010000000000000000000000000
    011010010000010010010111001111101011001001101110000000000000000000000100000000000000000000000000
    010010111010000000001101110001010010111111000110000000000000000000001000000000000000000000000000
    001101101110101101101010101101001010101001011001000000000000000000010000000000000000000000000000
    001011000111010011101110010011010101101001011011000000000000000000100000000000000000000000000000
    010001100000101001011101101010101001101001010011000000000000000001000000000000000000000000000000
    000000000100001110011011000010100111110000001101000000000000000010000000000000000000000000000000
    000000010000110101101100001010011111000000110100000000000000000100000000000000000000000000000000
    000001000011001110110000101001111100000011010000000000000000001000000000000000000000000000000000
    000100001100001011000010100111110000001101000000000000000000010000000000000000000000000000000000
    010000110001001100001010011111000000110100000000000000000000100000000000000000000000000000000000
    000101000001011101000100010100000010000101000001000000000001000000000000000000000000000000000000
    010100000011110100010001010000001000010100000100000000000010000000000000000000000000000000000000
    010110000101111100101000101000100000000101010001000000000100000000000000000000000000000000000000
    011110001001011111001111001010000001000000000101000000001000000000000000000000000000000000000000
    000011101110110101110101100111111010011001101010000000010000000000000000000000000000000000000000
    001111011011010111010110011111101001100110101000000000100000000000000000000000000000000000000000
    000011010000111001111101011001011001010110011111000001000000000000000000000000000000000000000000
    001011000011100111110101100101100101011001111100000010000000000000000000000000000000000000000000
    011101110011111011110010110001101010101011001111000100000000000000000000000000000000000000000000
    010100110100100110000010001001010100110101000010001000000000000000000000000000000000000000000000
    011000101001010001000001101010101101001101110110010000000000000000000000000000000000000000000000
Transform M into row reduced echelon form (rref)
M = 010000000000000000000000000000001000000000101011000000111100100000000111000010010001000010010010
    001000000000000000000000000000001000000000001001000000111100110101101111110011000101110101001010
    000100000000000000000000000000000000000010100001000000100011011101101110111101100000011100011100
    000010000000000000000000000000000000000000001000000000110000110110000011010000011010100011110010
    000001000000000000000000000000001000000000000011000000010110101111101101011011001010111100100100
    000000100000000000000000000000000000000000001011000000100111110000111101110010010101101001001100
    000000010000000000000000000000000000000000100000000000000000000000000000000100000000010000100000
    000000001000000000000000000000001000000010100000000000000010100110110001010001100010000010011010
    000000000100000000000000000000001000000000001001000000111111111100000000000101110011000100111010
    000000000010000000000000000000000000000000100011000000101100000111110111110010101100110011001100
    000000000001000000000000000000000000000010101000000000010011010100110111110110111011001110001110
    000000000000100000000000000000000000000010001010000000010010101011001000011001010111001011111100
    000000000000010000000000000000000000000010000000000000010011011000001111001111000100110011000110
    000000000000001000000000000000000000000000000010000000010111100011010101110010101111010101000100
    000000000000000100000000000000000000000000000010000000000000000000000000000000010000000100010110
    000000000000000010000000000000001000000010001000000000000101010111110000000111010000000010110000
    000000000000000001000000000000001000000000000000000000000000000000000000000000001000000000000000
    000000000000000000100000000000001000000010001000000000010001000011011010100011110010010101100010
    000000000000000000010000000000000000000010000000000000000000000000000000000000000100000010000000
    000000000000000000001000000000001000000000000000000000111001100111110000100101000010000110101010
    000000000000000000000100000000000000000010001010000000000111110011000110000110101110111110111110
    000000000000000000000010000000000000000000001000000000011100100111110010110110000000100100001110
    000000000000000000000001000000000000000000001000000000000000000000000000000000000001000001001000
    000000000000000000000000100000001000000000101011000000111100100000000111100010010001000010010010
    000000000000000000000000010000000000000010100001000000100011011101101110101101100000011100011100
    000000000000000000000000001000001000000000000011000000010110101111101101010011001010111100100100
    000000000000000000000000000100000000000000100000000000000000000000000000000000000000010000100000
    000000000000000000000000000010001000000000001001000000111111111100000000000111110011000100111010
    000000000000000000000000000001000000000010101000000000010011010100110111110111111011001110001110
    000000000000000000000000000000100000000010000000000000010011011000001111001111100100110011000110
    000000000000000000000000000000010000000000000010000000000000000000000000000000000000000100010110
    000000000000000000000000000000000100000010000000000000000000000000000000000000000000000010000000
    000000000000000000000000000000000010000010001010000000000111110011000110000110101100111110111110
    000000000000000000000000000000000001000000001000000000000000000000000000000000000000000001001000
    000000000000000000000000000000000000100010100001000000100011011101101110101101100000111100011100
    000000000000000000000000000000000000010000100000000000000000000000000000000000000000000000100000
    000000000000000000000000000000000000001010101000000000010011010100110111110111111011000110001110
    000000000000000000000000000000000000000100000010000000000000000000000000000000000000000000010110
    000000000000000000000000000000000000000001001000000000000000000000000000000000000000000000001000
    000000000000000000000000000000000000000000010010000000000000000000000000000000000000000000000110
    000000000000000000000000000000000000000000000110000000000000000000000000000000000000000000000010
    000000000000000000000000000000000000000000000000010000110000110000001110100101100010101100011000
    000000000000000000000000000000000000000000000000001000101010001100101010101101010001000010010010
    000000000000000000000000000000000000000000000000000100011011101100010010111000110111101000001100
    000000000000000000000000000000000000000000000000000010001011001011101101101010110001011000000000
    000000000000000000000000000000000000000000000000000001111001111000100100100010101110100111101100
    000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 10000000000000000000000000000001000000000101011 00000111100100000000111000010010001000010010010
    01000000000000000000000000000001000000000001001 00000111100110101101111110011000101110101001010
    00100000000000000000000000000000000000010100001 00000100011011101101110111101100000011100011100
    00010000000000000000000000000000000000000001000 00000110000110110000011010000011010100011110010
    00001000000000000000000000000001000000000000011 00000010110101111101101011011001010111100100100
    00000100000000000000000000000000000000000001011 00000100111110000111101110010010101101001001100
    00000010000000000000000000000000000000000100000 00000000000000000000000000100000000010000100000
    00000001000000000000000000000001000000010100000 00000000010100110110001010001100010000010011010
    00000000100000000000000000000001000000000001001 00000111111111100000000000101110011000100111010
    00000000010000000000000000000000000000000100011 00000101100000111110111110010101100110011001100
    00000000001000000000000000000000000000010101000 00000010011010100110111110110111011001110001110
    00000000000100000000000000000000000000010001010 00000010010101011001000011001010111001011111100
    00000000000010000000000000000000000000010000000 00000010011011000001111001111000100110011000110
    00000000000001000000000000000000000000000000010 00000010111100011010101110010101111010101000100
    00000000000000100000000000000000000000000000010 00000000000000000000000000000010000000100010110
    00000000000000010000000000000001000000010001000 00000000101010111110000000111010000000010110000
    00000000000000001000000000000001000000000000000 00000000000000000000000000000001000000000000000
    00000000000000000100000000000001000000010001000 00000010001000011011010100011110010010101100010
    00000000000000000010000000000000000000010000000 00000000000000000000000000000000100000010000000
    00000000000000000001000000000001000000000000000 00000111001100111110000100101000010000110101010
    00000000000000000000100000000000000000010001010 00000000111110011000110000110101110111110111110
    00000000000000000000010000000000000000000001000 00000011100100111110010110110000000100100001110
    00000000000000000000001000000000000000000001000 00000000000000000000000000000000001000001001000
    00000000000000000000000100000001000000000101011 00000111100100000000111100010010001000010010010
    00000000000000000000000010000000000000010100001 00000100011011101101110101101100000011100011100
    00000000000000000000000001000001000000000000011 00000010110101111101101010011001010111100100100
    00000000000000000000000000100000000000000100000 00000000000000000000000000000000000010000100000
    00000000000000000000000000010001000000000001001 00000111111111100000000000111110011000100111010
    00000000000000000000000000001000000000010101000 00000010011010100110111110111111011001110001110
    00000000000000000000000000000100000000010000000 00000010011011000001111001111100100110011000110
    00000000000000000000000000000010000000000000010 00000000000000000000000000000000000000100010110
    00000000000000000000000000000000100000010000000 00000000000000000000000000000000000000010000000
    00000000000000000000000000000000010000010001010 00000000111110011000110000110101100111110111110
    00000000000000000000000000000000001000000001000 00000000000000000000000000000000000000001001000
    00000000000000000000000000000000000100010100001 00000100011011101101110101101100000111100011100
    00000000000000000000000000000000000010000100000 00000000000000000000000000000000000000000100000
    00000000000000000000000000000000000001010101000 00000010011010100110111110111111011000110001110
    00000000000000000000000000000000000000100000010 00000000000000000000000000000000000000000010110
    00000000000000000000000000000000000000001001000 00000000000000000000000000000000000000000001000
    00000000000000000000000000000000000000000010010 00000000000000000000000000000000000000000000110
    00000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000000000 10000110000110000001110100101100010101100011000
    00000000000000000000000000000000000000000000000 01000101010001100101010101101010001000010010010
    00000000000000000000000000000000000000000000000 00100011011101100010010111000110111101000001100
    00000000000000000000000000000000000000000000000 00010001011001011101101101010110001011000000000
    00000000000000000000000000000000000000000000000 00001111001111000100100100010101110100111101100
    00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 10000000000000000000000000000001000000000101011 00000111100100000000111000010010001000010010010
    01000000000000000000000000000001000000000001001 00000111100110101101111110011000101110101001010
    00100000000000000000000000000000000000010100001 00000100011011101101110111101100000011100011100
    00010000000000000000000000000000000000000001000 00000110000110110000011010000011010100011110010
    00001000000000000000000000000001000000000000011 00000010110101111101101011011001010111100100100
    00000100000000000000000000000000000000000001011 00000100111110000111101110010010101101001001100
    00000010000000000000000000000000000000000100000 00000000000000000000000000100000000010000100000
    00000001000000000000000000000001000000010100000 00000000010100110110001010001100010000010011010
    00000000100000000000000000000001000000000001001 00000111111111100000000000101110011000100111010
    00000000010000000000000000000000000000000100011 00000101100000111110111110010101100110011001100
    00000000001000000000000000000000000000010101000 00000010011010100110111110110111011001110001110
    00000000000100000000000000000000000000010001010 00000010010101011001000011001010111001011111100
    00000000000010000000000000000000000000010000000 00000010011011000001111001111000100110011000110
    00000000000001000000000000000000000000000000010 00000010111100011010101110010101111010101000100
    00000000000000100000000000000000000000000000010 00000000000000000000000000000010000000100010110
    00000000000000010000000000000001000000010001000 00000000101010111110000000111010000000010110000
    00000000000000001000000000000001000000000000000 00000000000000000000000000000001000000000000000
    00000000000000000100000000000001000000010001000 00000010001000011011010100011110010010101100010
    00000000000000000010000000000000000000010000000 00000000000000000000000000000000100000010000000
    00000000000000000001000000000001000000000000000 00000111001100111110000100101000010000110101010
    00000000000000000000100000000000000000010001010 00000000111110011000110000110101110111110111110
    00000000000000000000010000000000000000000001000 00000011100100111110010110110000000100100001110
    00000000000000000000001000000000000000000001000 00000000000000000000000000000000001000001001000
    00000000000000000000000100000001000000000101011 00000111100100000000111100010010001000010010010
    00000000000000000000000010000000000000010100001 00000100011011101101110101101100000011100011100
    00000000000000000000000001000001000000000000011 00000010110101111101101010011001010111100100100
    00000000000000000000000000100000000000000100000 00000000000000000000000000000000000010000100000
    00000000000000000000000000010001000000000001001 00000111111111100000000000111110011000100111010
    00000000000000000000000000001000000000010101000 00000010011010100110111110111111011001110001110
    00000000000000000000000000000100000000010000000 00000010011011000001111001111100100110011000110
    00000000000000000000000000000010000000000000010 00000000000000000000000000000000000000100010110
    00000000000000000000000000000000100000010000000 00000000000000000000000000000000000000010000000
    00000000000000000000000000000000010000010001010 00000000111110011000110000110101100111110111110
    00000000000000000000000000000000001000000001000 00000000000000000000000000000000000000001001000
    00000000000000000000000000000000000100010100001 00000100011011101101110101101100000111100011100
    00000000000000000000000000000000000010000100000 00000000000000000000000000000000000000000100000
    00000000000000000000000000000000000001010101000 00000010011010100110111110111111011000110001110
    00000000000000000000000000000000000000100000010 00000000000000000000000000000000000000000010110
    00000000000000000000000000000000000000001001000 00000000000000000000000000000000000000000001000
    00000000000000000000000000000000000000000010010 00000000000000000000000000000000000000000000110
    00000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000000000 10000110000110000001110100101100010101100011000
    00000000000000000000000000000000000000000000000 01000101010001100101010101101010001000010010010
    00000000000000000000000000000000000000000000000 00100011011101100010010111000110111101000001100
    00000000000000000000000000000000000000000000000 00010001011001011101101101010110001011000000000
    00000000000000000000000000000000000000000000000 00001111001111000100100100010101110100111101100
    00000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000001
Null basis vectors

nv0 = b0000000000000000010000110000110000001110100101100010101100011000
nv0 = 0x0000430c0e962b18
nv0 = x46 + x41 + x40 + x35 + x34 + x27 + x26 + x25 + x23 + x20 + x18 + x17 + x13 + x11 + x9 + x8 + x4 + x3

nv1 = b0000000000000000001000101010001100101010101101010001000010010010
nv1 = 0x000022a32ab51092
nv1 = x45 + x41 + x39 + x37 + x33 + x32 + x29 + x27 + x25 + x23 + x21 + x20 + x18 + x16 + x12 + x7 + x4 + x

nv2 = b0000000000000000000100011011101100010010111000110111101000001100
nv2 = 0x000011bb12e37a0c
nv2 = x44 + x40 + x39 + x37 + x36 + x35 + x33 + x32 + x28 + x25 + x23 + x22 + x21 + x17 + x16 + x14 + x13 + x12 + x11 + x9 + x3 + x2

nv3 = b0000000000000000000010001011001011101101101010110001011000000000
nv3 = 0x000008b2edab1600
nv3 = x43 + x39 + x37 + x36 + x33 + x31 + x30 + x29 + x27 + x26 + x24 + x23 + x21 + x19 + x17 + x16 + x12 + x10 + x9

nv4 = b0000000000000000000001111001111000100100100010101110100111101100
nv4 = 0x0000079e248ae9ec
nv4 = x42 + x41 + x40 + x39 + x36 + x35 + x34 + x33 + x29 + x26 + x23 + x19 + x17 + x15 + x14 + x13 + x11 + x8 + x7 + x6 + x5 + x3 + x2

nv5 = b0000000000000000000000000000000000000000000000000000000000000001
nv5 = 0x0000000000000001
nv5 = 1

See also: