gf(2) Find null basis vectors of M

M = 000000000000000000000000000000000000000000000000000000000000000
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    000000000000000000000000000000000000000000000000100000010000000
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    100111001001010100011001100111001001111111110000001100100110000
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    000110001111101001100101101110110110111010100100010100100011001
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    110011010001111000111101011001011010010101101001001100000101100
    010011011011101101010110010010011001001110011010000111110000110
    100010100000110010110100110010011100110101110111000100110000011
    111011010001000011010101000101111011000011111101111111010100001
    110011011000000000101111100000011100010111001001001010110110010
    010011111100001010000101110110000001000100011010011100111111110
    100000111110100011001010100011111100011101110110101000001100011
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    010100111101001010001011111000010110010111010010000101110110010
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    010000101011100011001101010101001001011111110000011011100101000
    100010101110001100110101010100100101111111000001101110010100000
Augment M with identity (I) of same size
M = 000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001
    000000000000000000000000000000000000000000000000000000000000110 000000000000000000000000000000000000000000000000000000000000010
    000000000000000000000000000000000000000000000000000000000010100 000000000000000000000000000000000000000000000000000000000000100
    000000000000000000000000000000000000000000000000000000001001000 000000000000000000000000000000000000000000000000000000000001000
    000000000000000000000000000000000000000000000000000000100010000 000000000000000000000000000000000000000000000000000000000010000
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    000000000000000000000000000000000000000000000000001000001000000 000000000000000000000000000000000000000000000000000000001000000
    000000000000000000000000000000000000000000000000100000010000000 000000000000000000000000000000000000000000000000000000010000000
    000000000000000000000000000000000000000000000010000000100000000 000000000000000000000000000000000000000000000000000000100000000
    000000000000000000000000000000000000000000001000000001000000000 000000000000000000000000000000000000000000000000000001000000000
    000000000000000000000000000000000000000000100000000010000000000 000000000000000000000000000000000000000000000000000010000000000
    000000000000000000000000000000000000000010000000000100000000000 000000000000000000000000000000000000000000000000000100000000000
    000000000000000000000000000000000000001000000000001000000000000 000000000000000000000000000000000000000000000000001000000000000
    000000000000000000000000000000000000100000000000010000000000000 000000000000000000000000000000000000000000000000010000000000000
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    000000000000000000000000000000100000000000000010000000000000000 000000000000000000000000000000000000000000000010000000000000000
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    000000000000000000000000001000000000000000001000000000000000000 000000000000000000000000000000000000000000001000000000000000000
    000000000000000000000000100000000000000000010000000000000000000 000000000000000000000000000000000000000000010000000000000000000
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    000000000000000000001000000000000000000001000000000000000000000 000000000000000000000000000000000000000001000000000000000000000
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    011011010100101000100011000110010001001010111000000110110000010 000000000000000000000000000001000000000000000000000000000000000
    000010011100100101010001100100111100100111111111000000110010011 000000000000000000000000000010000000000000000000000000000000000
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    101101110111011000000000100000101111101011100001011110001101101 000000000000000000000000010000000000000000000000000000000000000
    000110001111101001100101101110110110111010100100010100100011001 000000000000000000000000100000000000000000000000000000000000000
    011000111110100110010101111011011011101010010001010010001100100 000000000000000000000001000000000000000000000000000000000000000
    001100110100011110001100010110010110100101011010010011000001011 000000000000000000000010000000000000000000000000000000000000000
    110011010001111000111101011001011010010101101001001100000101100 000000000000000000000100000000000000000000000000000000000000000
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    100010100000110010110100110010011100110101110111000100110000011 000000000000000000010000000000000000000000000000000000000000000
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    110011011000000000101111100000011100010111001001001010110110010 000000000000000001000000000000000000000000000000000000000000000
    010011111100001010000101110110000001000100011010011100111111110 000000000000000010000000000000000000000000000000000000000000000
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M expressed in convenient bit depth
M = 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
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Transform M into row reduced echelon form (rref)
M = 01000000000000000000000000000000000000000000000000000000000000000110010110010100110100110110110011000011101100010111100111010010
    00100000000000000000000000000000000000000000000000000000000000010001000100001101100000111110001011101110000101100010000101001000
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    00000001000000000000000000000000000000000000000000000000000000010111010111111010110100100000011010000010110101100010011110101000
    00000000100000000000000000000000000000000000000000000000000000000110000100001010100110001111011111011000000101000001010110000000
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    00000000001000000000000000000000000000000000000000000000000000000000010111010000000100001011001011101111100000100011010100111100
    00000000000100000000000000000000000000000000000000000000000000010101000001110010111101011010000101001101010100011111001111110100
    00000000000010000000000000000000000000000000000000000000000000010111111101000001101100001110000100110000111001000101000011010010
    00000000000001000000000000000000000000000000000000000000000000010110100000011011111001101100110101000000001101010110001000010000
    00000000000000100000000000000000000000000000000000000000000000010111010011010110000111111011110000001101000010100100011111111100
    00000000000000010000000000000000000000000000000000000000000000000011111111000101101001000101100101111111111100010011110100001110
    00000000000000001000000000000000000000000000000000000000000000010110100001110001100010101111001111110001001100010000000100001010
    00000000000000000100000000000000000000000000000000000000000000010001001001101101011111100000010001011101010010111010010010000110
    00000000000000000010000000000000000000000000000000000000000000010011010111010011110000110101101111011110000100010000101111110010
    00000000000000000001000000000000000000000000000000000000000000010111010001000100010010010100001101101110001001000101110101000110
    00000000000000000000100000000000000000000000000000000000000000010101011110010100101110100100110111100101110100110111100110101000
    00000000000000000000010000000000000000000000000000000000000000000010100110011111001110110001111100111101010110101111011101101010
    00000000000000000000001000000000000000000000000000000000000000000110111110001111100011101000010100011110011111111000110111101100
    00000000000000000000000100000000000000000000000000000000000000000010011001100010010100000110111101110110010110011011100111001010
    00000000000000000000000010000000000000000000000000000000000000000011101100010011001011101001100000110110111001111101110010011100
    00000000000000000000000001000000000000000000000000000000000000000110010010011001111101010111110101000000011010010001010101000010
    00000000000000000000000000100000000000000000000000000000000000010011110010111001100101111001101000001000100010000001100100011110
    00000000000000000000000000010000000000000000000000000000000000010000110100000101000101001111000100100110011111000000001010100110
    00000000000000000000000000001000000000000000000000000000000000000100010110010101011001010000000000111010010111100110110011101010
    00000000000000000000000000000100000000000000000000000000000000000011001101101100110000111000100001111000111000100000011101010110
    00000000000000000000000000000010000000000000000000000000000000000111100000101001000100010000110100101001000001110110101000111110
    00000000000000000000000000000001000000000000000000000000000000010010111111111011001010100011111101001110100001111101111101100100
    00000000000000000000000000000000100000000000000000000000000000000110010110010100110100110110110001000011101100010111100111010010
    00000000000000000000000000000000010000000000000000000000000000000111000001111000000101110001001011110001100111110010000100010000
    00000000000000000000000000000000001000000000000000000000000000010111111101011101011001011110001011001001100111110000110100110100
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    00000000000000000000000000000000000010000000000000000000000000010100000000101011100000110100101101101001010101001000000001110110
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    00000000000000000000000000000000000000010000000000000000000000000011111111000101101001000101100101111110111100010011110100001110
    00000000000000000000000000000000000000001000000000000000000000010001001001101101011111100000010001011101110010111010010010000110
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    00000000000000000000000000000000000000000010000000000000000000000010100110011111001110110001111100111101011110101111011101101010
    00000000000000000000000000000000000000000001000000000000000000000010011001100010010100000110111101110110010010011011100111001010
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    00000000000000000000000000000000000000000000000010000000000000000111000001111000000101110001001011110001100111111010000100010000
    00000000000000000000000000000000000000000000000001000000000000010111010111111010110100100000011010010010110101100110011110101000
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    00000000000000000000000000000000000000000000000000010000000000000011111111000101101001000101100101111110111100010010110100001110
    00000000000000000000000000000000000000000000000000001000000000010111010001000100010010010100001101101110011001000101010101000110
    00000000000000000000000000000000000000000000000000000100000000000010011001100010010100000110111101110110010010011011110111001010
    00000000000000000000000000000000000000000000000000000010000000010000110100000101000101001111000100100110011110000000000010100110
    00000000000000000000000000000000000000000000000000000001000000010010111111111011001010100011111101001110100001101101111001100100
    00000000000000000000000000000000000000000000000000000000100000010111010111111010110100100000011010010010110101100110011100101000
    00000000000000000000000000000000000000000000000000000000010000000011111111000101101001000101100101111110111100010010110101001110
    00000000000000000000000000000000000000000000000000000000001000000010011001100010010100000110111101110110010010011011110111101010
    00000000000000000000000000000000000000000000000000000000000100010010111111111011001010100011111101001110100001101101111001110100
    00000000000000000000000000000000000000000000000000000000000010000011111111000101101001000101100101111110111100010010110101000110
    00000000000000000000000000000000000000000000000000000000000001010010111111111011001010100011111101001110100001101101111001110000
    00000000000000000000000000000000000000000000000000000000000000110010111111111011001010100011111101001110100001101101111001110010
    00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 100000000000000000000000000000000000000000000000000000000000000 110010110010100110100110110110011000011101100010111100111010010
    010000000000000000000000000000000000000000000000000000000000001 001000100001101100000111110001011101110000101100010000101001000
    001000000000000000000000000000000000000000000000000000000000000 111000001111000000101110001001010110001100111110010000100010000
    000100000000000000000000000000000000000000000000000000000000001 111010111111000101001110001001110000011110111110101011100100100
    000010000000000000000000000000000000000000000000000000000000001 111111101011101011001011110001011101001100111110000110100110100
    000001000000000000000000000000000000000000000000000000000000001 011010011111100011011010000100101110010101110011001100100010010
    000000100000000000000000000000000000000000000000000000000000001 111010111111010110100100000011010000010110101100010011110101000
    000000010000000000000000000000000000000000000000000000000000000 110000100001010100110001111011111011000000101000001010110000000
    000000001000000000000000000000000000000000000000000000000000001 100000000101011100000110100101101100001010101001000000001110110
    000000000100000000000000000000000000000000000000000000000000000 000010111010000000100001011001011101111100000100011010100111100
    000000000010000000000000000000000000000000000000000000000000001 101000001110010111101011010000101001101010100011111001111110100
    000000000001000000000000000000000000000000000000000000000000001 111111101000001101100001110000100110000111001000101000011010010
    000000000000100000000000000000000000000000000000000000000000001 110100000011011111001101100110101000000001101010110001000010000
    000000000000010000000000000000000000000000000000000000000000001 111010011010110000111111011110000001101000010100100011111111100
    000000000000001000000000000000000000000000000000000000000000000 011111111000101101001000101100101111111111100010011110100001110
    000000000000000100000000000000000000000000000000000000000000001 110100001110001100010101111001111110001001100010000000100001010
    000000000000000010000000000000000000000000000000000000000000001 001001001101101011111100000010001011101010010111010010010000110
    000000000000000001000000000000000000000000000000000000000000001 011010111010011110000110101101111011110000100010000101111110010
    000000000000000000100000000000000000000000000000000000000000001 111010001000100010010010100001101101110001001000101110101000110
    000000000000000000010000000000000000000000000000000000000000001 101011110010100101110100100110111100101110100110111100110101000
    000000000000000000001000000000000000000000000000000000000000000 010100110011111001110110001111100111101010110101111011101101010
    000000000000000000000100000000000000000000000000000000000000000 110111110001111100011101000010100011110011111111000110111101100
    000000000000000000000010000000000000000000000000000000000000000 010011001100010010100000110111101110110010110011011100111001010
    000000000000000000000001000000000000000000000000000000000000000 011101100010011001011101001100000110110111001111101110010011100
    000000000000000000000000100000000000000000000000000000000000000 110010010011001111101010111110101000000011010010001010101000010
    000000000000000000000000010000000000000000000000000000000000001 011110010111001100101111001101000001000100010000001100100011110
    000000000000000000000000001000000000000000000000000000000000001 000110100000101000101001111000100100110011111000000001010100110
    000000000000000000000000000100000000000000000000000000000000000 100010110010101011001010000000000111010010111100110110011101010
    000000000000000000000000000010000000000000000000000000000000000 011001101101100110000111000100001111000111000100000011101010110
    000000000000000000000000000001000000000000000000000000000000000 111100000101001000100010000110100101001000001110110101000111110
    000000000000000000000000000000100000000000000000000000000000001 010111111111011001010100011111101001110100001111101111101100100
    000000000000000000000000000000010000000000000000000000000000000 110010110010100110100110110110001000011101100010111100111010010
    000000000000000000000000000000001000000000000000000000000000000 111000001111000000101110001001011110001100111110010000100010000
    000000000000000000000000000000000100000000000000000000000000001 111111101011101011001011110001011001001100111110000110100110100
    000000000000000000000000000000000010000000000000000000000000001 111010111111010110100100000011010010010110101100010011110101000
    000000000000000000000000000000000001000000000000000000000000001 100000000101011100000110100101101101001010101001000000001110110
    000000000000000000000000000000000000100000000000000000000000001 101000001110010111101011010000101001001010100011111001111110100
    000000000000000000000000000000000000010000000000000000000000001 110100000011011111001101100110101000010001101010110001000010000
    000000000000000000000000000000000000001000000000000000000000000 011111111000101101001000101100101111110111100010011110100001110
    000000000000000000000000000000000000000100000000000000000000001 001001001101101011111100000010001011101110010111010010010000110
    000000000000000000000000000000000000000010000000000000000000001 111010001000100010010010100001101101110011001000101110101000110
    000000000000000000000000000000000000000001000000000000000000000 010100110011111001110110001111100111101011110101111011101101010
    000000000000000000000000000000000000000000100000000000000000000 010011001100010010100000110111101110110010010011011100111001010
    000000000000000000000000000000000000000000010000000000000000000 110010010011001111101010111110101000000011000010001010101000010
    000000000000000000000000000000000000000000001000000000000000001 000110100000101000101001111000100100110011110000000001010100110
    000000000000000000000000000000000000000000000100000000000000000 011001101101100110000111000100001111000111000000000011101010110
    000000000000000000000000000000000000000000000010000000000000001 010111111111011001010100011111101001110100001101101111101100100
    000000000000000000000000000000000000000000000001000000000000000 111000001111000000101110001001011110001100111111010000100010000
    000000000000000000000000000000000000000000000000100000000000001 111010111111010110100100000011010010010110101100110011110101000
    000000000000000000000000000000000000000000000000010000000000001 101000001110010111101011010000101001001010100011101001111110100
    000000000000000000000000000000000000000000000000001000000000000 011111111000101101001000101100101111110111100010010110100001110
    000000000000000000000000000000000000000000000000000100000000001 111010001000100010010010100001101101110011001000101010101000110
    000000000000000000000000000000000000000000000000000010000000000 010011001100010010100000110111101110110010010011011110111001010
    000000000000000000000000000000000000000000000000000001000000001 000110100000101000101001111000100100110011110000000000010100110
    000000000000000000000000000000000000000000000000000000100000001 010111111111011001010100011111101001110100001101101111001100100
    000000000000000000000000000000000000000000000000000000010000001 111010111111010110100100000011010010010110101100110011100101000
    000000000000000000000000000000000000000000000000000000001000000 011111111000101101001000101100101111110111100010010110101001110
    000000000000000000000000000000000000000000000000000000000100000 010011001100010010100000110111101110110010010011011110111101010
    000000000000000000000000000000000000000000000000000000000010001 010111111111011001010100011111101001110100001101101111001110100
    000000000000000000000000000000000000000000000000000000000001000 011111111000101101001000101100101111110111100010010110101000110
    000000000000000000000000000000000000000000000000000000000000101 010111111111011001010100011111101001110100001101101111001110000
    000000000000000000000000000000000000000000000000000000000000011 010111111111011001010100011111101001110100001101101111001110010
    000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 100000000000000000000000000000000000000000000000000000000000000 110010110010100110100110110110011000011101100010111100111010010
    010000000000000000000000000000000000000000000000000000000000001 001000100001101100000111110001011101110000101100010000101001000
    001000000000000000000000000000000000000000000000000000000000000 111000001111000000101110001001010110001100111110010000100010000
    000100000000000000000000000000000000000000000000000000000000001 111010111111000101001110001001110000011110111110101011100100100
    000010000000000000000000000000000000000000000000000000000000001 111111101011101011001011110001011101001100111110000110100110100
    000001000000000000000000000000000000000000000000000000000000001 011010011111100011011010000100101110010101110011001100100010010
    000000100000000000000000000000000000000000000000000000000000001 111010111111010110100100000011010000010110101100010011110101000
    000000010000000000000000000000000000000000000000000000000000000 110000100001010100110001111011111011000000101000001010110000000
    000000001000000000000000000000000000000000000000000000000000001 100000000101011100000110100101101100001010101001000000001110110
    000000000100000000000000000000000000000000000000000000000000000 000010111010000000100001011001011101111100000100011010100111100
    000000000010000000000000000000000000000000000000000000000000001 101000001110010111101011010000101001101010100011111001111110100
    000000000001000000000000000000000000000000000000000000000000001 111111101000001101100001110000100110000111001000101000011010010
    000000000000100000000000000000000000000000000000000000000000001 110100000011011111001101100110101000000001101010110001000010000
    000000000000010000000000000000000000000000000000000000000000001 111010011010110000111111011110000001101000010100100011111111100
    000000000000001000000000000000000000000000000000000000000000000 011111111000101101001000101100101111111111100010011110100001110
    000000000000000100000000000000000000000000000000000000000000001 110100001110001100010101111001111110001001100010000000100001010
    000000000000000010000000000000000000000000000000000000000000001 001001001101101011111100000010001011101010010111010010010000110
    000000000000000001000000000000000000000000000000000000000000001 011010111010011110000110101101111011110000100010000101111110010
    000000000000000000100000000000000000000000000000000000000000001 111010001000100010010010100001101101110001001000101110101000110
    000000000000000000010000000000000000000000000000000000000000001 101011110010100101110100100110111100101110100110111100110101000
    000000000000000000001000000000000000000000000000000000000000000 010100110011111001110110001111100111101010110101111011101101010
    000000000000000000000100000000000000000000000000000000000000000 110111110001111100011101000010100011110011111111000110111101100
    000000000000000000000010000000000000000000000000000000000000000 010011001100010010100000110111101110110010110011011100111001010
    000000000000000000000001000000000000000000000000000000000000000 011101100010011001011101001100000110110111001111101110010011100
    000000000000000000000000100000000000000000000000000000000000000 110010010011001111101010111110101000000011010010001010101000010
    000000000000000000000000010000000000000000000000000000000000001 011110010111001100101111001101000001000100010000001100100011110
    000000000000000000000000001000000000000000000000000000000000001 000110100000101000101001111000100100110011111000000001010100110
    000000000000000000000000000100000000000000000000000000000000000 100010110010101011001010000000000111010010111100110110011101010
    000000000000000000000000000010000000000000000000000000000000000 011001101101100110000111000100001111000111000100000011101010110
    000000000000000000000000000001000000000000000000000000000000000 111100000101001000100010000110100101001000001110110101000111110
    000000000000000000000000000000100000000000000000000000000000001 010111111111011001010100011111101001110100001111101111101100100
    000000000000000000000000000000010000000000000000000000000000000 110010110010100110100110110110001000011101100010111100111010010
    000000000000000000000000000000001000000000000000000000000000000 111000001111000000101110001001011110001100111110010000100010000
    000000000000000000000000000000000100000000000000000000000000001 111111101011101011001011110001011001001100111110000110100110100
    000000000000000000000000000000000010000000000000000000000000001 111010111111010110100100000011010010010110101100010011110101000
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Null basis vectors

nv0 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
nv0 = 0x00000000000000000000000000000001
nv0 = 1

See also: