gf(2) Find null basis vectors of M

M = 000000000000000000000000000000000000000000000000000000000000000
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    000000000000000000000000000000000000000000000000100000010000000
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    100100100010111111110111001000100100000010000001100011110010101
Augment M with identity (I) of same size
M = 000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001
    000000000000000000000000000000000000000000000000000000000000110 000000000000000000000000000000000000000000000000000000000000010
    000000000000000000000000000000000000000000000000000000000010100 000000000000000000000000000000000000000000000000000000000000100
    000000000000000000000000000000000000000000000000000000001001000 000000000000000000000000000000000000000000000000000000000001000
    000000000000000000000000000000000000000000000000000000100010000 000000000000000000000000000000000000000000000000000000000010000
    000000000000000000000000000000000000000000000000000010000100000 000000000000000000000000000000000000000000000000000000000100000
    000000000000000000000000000000000000000000000000001000001000000 000000000000000000000000000000000000000000000000000000001000000
    000000000000000000000000000000000000000000000000100000010000000 000000000000000000000000000000000000000000000000000000010000000
    000000000000000000000000000000000000000000000010000000100000000 000000000000000000000000000000000000000000000000000000100000000
    000000000000000000000000000000000000000000001000000001000000000 000000000000000000000000000000000000000000000000000001000000000
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    000000000000000000000000000000000000000010000000000100000000000 000000000000000000000000000000000000000000000000000100000000000
    000000000000000000000000000000000000001000000000001000000000000 000000000000000000000000000000000000000000000000001000000000000
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    010001101000001101111100000011011010010000100110110000110001000 000000000000000000000000000100000000000000000000000000000000000
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    101111011110010010000110111000100010010111000010001001001111100 000000000000000000000000010000000000000000000000000000000000000
    100111010111101110111001101101001010010011011111100110010001110 000000000000000000000000100000000000000000000000000000000000000
    000111110000011101000110011011101010000010101001011011101000110 000000000000000000000001000000000000000000000000000000000000000
    011111000001110100011111101110101000001010100101101110100011000 000000000000000000000010000000000000000000000000000000000000000
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    011111011110000010100001001001011110011110100001001110101000010 000000000000000010000000000000000000000000000000000000000000000
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    100100100010111111110111001000100100000010000001100011110010101 100000000000000000000000000000000000000000000000000000000000000
M expressed in convenient bit depth
M = 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
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Transform M into row reduced echelon form (rref)
M = 01000000000000000000000000000000000000000000000000000000000000000010111101101001011111000101110110100110101011001110010101100100
    00100000000000000000000000000000000000000000000000000000000000010011011010011001011101001010100100101001110001110000101101110010
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    00000001000000000000000000000000000000000000000000000000000000010100001001000000000000000100101101110110111001001111110110010010
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    00000000000100000000000000000000000000000000000000000000000000000010000010010100010010001011100110001111000100011101110000011100
    00000000000010000000000000000000000000000000000000000000000000010111111010011010110000111010000110111000110111101000111010011010
    00000000000001000000000000000000000000000000000000000000000000000100000011111011111100110111011000010010100110000001100111100100
    00000000000000100000000000000000000000000000000000000000000000010100110110100101100100111011101000100100111110010111011111000100
    00000000000000010000000000000000000000000000000000000000000000010110011100100101110011010001000001110011111110010011111100011100
    00000000000000001000000000000000000000000000000000000000000000010010010000111111111111100100110000000000001101011000001011111000
    00000000000000000100000000000000000000000000000000000000000000000101000100101001111001100011111110110010010001000101111001011000
    00000000000000000010000000000000000000000000000000000000000000000101000100010010011101111111111100001111110010000111010011110100
    00000000000000000001000000000000000000000000000000000000000000010001110101000001010010011010111101010100101010010110111001101100
    00000000000000000000100000000000000000000000000000000000000000010100100011010110000110010100100110000001010100001100111111000000
    00000000000000000000010000000000000000000000000000000000000000010101001101111001111000000001110100000100100010011111101101100100
    00000000000000000000001000000000000000000000000000000000000000000111000011110011100111110010001011010111010001000001010010101010
    00000000000000000000000100000000000000000000000000000000000000000011100111100101001100001001101010110111101001100000011110100010
    00000000000000000000000010000000000000000000000000000000000000000000101001011111011010010101101101100111111010110101110101110000
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    00000000000000000000000000100000000000000000000000000000000000010100001000001001001000011100001011110110000011101011111001001000
    00000000000000000000000000010000000000000000000000000000000000000101110000011001110001111100101101110100100101111101001101101010
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    00000000000000000000000000000000000000001000000000000000000000000101000100101001111001100011111110110010110001000101111001011000
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    00000000000000000000000000000000000000000000000000001000000000010001110101000001010010011010111101010100111010010110011001101100
    00000000000000000000000000000000000000000000000000000100000000000011100111100101001100001001101010110111101101100000001110100010
    00000000000000000000000000000000000000000000000000000010000000000101110000011001110001111100101101110100100100111101000101101010
    00000000000000000000000000000000000000000000000000000001000000000000110001010011110010000100011111010101110001000100000001101100
    00000000000000000000000000000000000000000000000000000000100000010100001001000000000000000100101101100110111001001011110100010010
    00000000000000000000000000000000000000000000000000000000010000010110011100100101110011010001000001110010111110010010111101011100
    00000000000000000000000000000000000000000000000000000000001000000011100111100101001100001001101010110111101101100000001110000010
    00000000000000000000000000000000000000000000000000000000000100000000110001010011110010000100011111010101110001000100000001111100
    00000000000000000000000000000000000000000000000000000000000010010110011100100101110011010001000001110010111110010010111101010100
    00000000000000000000000000000000000000000000000000000000000001000000110001010011110010000100011111010101110001000100000001111000
    00000000000000000000000000000000000000000000000000000000000000100000110001010011110010000100011111010101110001000100000001111010
    00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 100000000000000000000000000000000000000000000000000000000000000 010111101101001011111000101110110100110101011001110010101100100
    010000000000000000000000000000000000000000000000000000000000001 011011010011001011101001010100100101001110001110000101101110010
    001000000000000000000000000000000000000000000000000000000000000 100010001100111111000101111111011000011001000110111011001111100
    000100000000000000000000000000000000000000000000000000000000001 010110111001100111110000110110010111110000101010100001010010100
    000010000000000000000000000000000000000000000000000000000000001 001100000010011000000110101110110001011111001000000100011110100
    000001000000000000000000000000000000000000000000000000000000000 100111001011100101000110101010011100100001100100110010110000110
    000000100000000000000000000000000000000000000000000000000000001 100001001000000000000000100101101110110111001001111110110010010
    000000010000000000000000000000000000000000000000000000000000000 110111111111011101111101111000100000001110111100000110001000000
    000000001000000000000000000000000000000000000000000000000000000 110000101100101010101000111101100001010100101110101101010101000
    000000000100000000000000000000000000000000000000000000000000000 001011010000000101110100000000100100111111111100110111001111110
    000000000010000000000000000000000000000000000000000000000000000 010000010010100010010001011100110001111000100011101110000011100
    000000000001000000000000000000000000000000000000000000000000001 111111010011010110000111010000110111000110111101000111010011010
    000000000000100000000000000000000000000000000000000000000000000 100000011111011111100110111011000010010100110000001100111100100
    000000000000010000000000000000000000000000000000000000000000001 100110110100101100100111011101000100100111110010111011111000100
    000000000000001000000000000000000000000000000000000000000000001 110011100100101110011010001000001110011111110010011111100011100
    000000000000000100000000000000000000000000000000000000000000001 010010000111111111111100100110000000000001101011000001011111000
    000000000000000010000000000000000000000000000000000000000000000 101000100101001111001100011111110110010010001000101111001011000
    000000000000000001000000000000000000000000000000000000000000000 101000100010010011101111111111100001111110010000111010011110100
    000000000000000000100000000000000000000000000000000000000000001 001110101000001010010011010111101010100101010010110111001101100
    000000000000000000010000000000000000000000000000000000000000001 100100011010110000110010100100110000001010100001100111111000000
    000000000000000000001000000000000000000000000000000000000000001 101001101111001111000000001110100000100100010011111101101100100
    000000000000000000000100000000000000000000000000000000000000000 111000011110011100111110010001011010111010001000001010010101010
    000000000000000000000010000000000000000000000000000000000000000 011100111100101001100001001101010110111101001100000011110100010
    000000000000000000000001000000000000000000000000000000000000000 000101001011111011010010101101101100111111010110101110101110000
    000000000000000000000000100000000000000000000000000000000000000 111110011111110011001000001000101000110000010011101110100011100
    000000000000000000000000010000000000000000000000000000000000001 100001000001001001000011100001011110110000011101011111001001000
    000000000000000000000000001000000000000000000000000000000000000 101110000011001110001111100101101110100100101111101001101101010
    000000000000000000000000000100000000000000000000000000000000000 000111110110001000010110110001011000100001110010000101110111010
    000000000000000000000000000010000000000000000000000000000000000 000100100010010010010011011100011110011011110110001101011010010
    000000000000000000000000000001000000000000000000000000000000001 010100000010100001100000001001001010110000110011110110010111000
    000000000000000000000000000000100000000000000000000000000000000 000110001010011110010000100011111010101110001010100000101101100
    000000000000000000000000000000010000000000000000000000000000000 010111101101001011111000101110100100110101011001110010101100100
    000000000000000000000000000000001000000000000000000000000000000 100010001100111111000101111111010000011001000110111011001111100
    000000000000000000000000000000000100000000000000000000000000001 001100000010011000000110101110110101011111001000000100011110100
    000000000000000000000000000000000010000000000000000000000000001 100001001000000000000000100101101100110111001001111110110010010
    000000000000000000000000000000000001000000000000000000000000000 110000101100101010101000111101100000010100101110101101010101000
    000000000000000000000000000000000000100000000000000000000000000 010000010010100010010001011100110001011000100011101110000011100
    000000000000000000000000000000000000010000000000000000000000000 100000011111011111100110111011000010000100110000001100111100100
    000000000000000000000000000000000000001000000000000000000000001 110011100100101110011010001000001110010111110010011111100011100
    000000000000000000000000000000000000000100000000000000000000000 101000100101001111001100011111110110010110001000101111001011000
    000000000000000000000000000000000000000010000000000000000000001 001110101000001010010011010111101010100111010010110111001101100
    000000000000000000000000000000000000000001000000000000000000001 101001101111001111000000001110100000100101010011111101101100100
    000000000000000000000000000000000000000000100000000000000000000 011100111100101001100001001101010110111101101100000011110100010
    000000000000000000000000000000000000000000010000000000000000000 111110011111110011001000001000101000110000000011101110100011100
    000000000000000000000000000000000000000000001000000000000000000 101110000011001110001111100101101110100100100111101001101101010
    000000000000000000000000000000000000000000000100000000000000000 000100100010010010010011011100011110011011110010001101011010010
    000000000000000000000000000000000000000000000010000000000000000 000110001010011110010000100011111010101110001000100000101101100
    000000000000000000000000000000000000000000000001000000000000000 100010001100111111000101111111010000011001000111111011001111100
    000000000000000000000000000000000000000000000000100000000000001 100001001000000000000000100101101100110111001001011110110010010
    000000000000000000000000000000000000000000000000010000000000000 010000010010100010010001011100110001011000100011111110000011100
    000000000000000000000000000000000000000000000000001000000000001 110011100100101110011010001000001110010111110010010111100011100
    000000000000000000000000000000000000000000000000000100000000001 001110101000001010010011010111101010100111010010110011001101100
    000000000000000000000000000000000000000000000000000010000000000 011100111100101001100001001101010110111101101100000001110100010
    000000000000000000000000000000000000000000000000000001000000000 101110000011001110001111100101101110100100100111101000101101010
    000000000000000000000000000000000000000000000000000000100000000 000110001010011110010000100011111010101110001000100000001101100
    000000000000000000000000000000000000000000000000000000010000001 100001001000000000000000100101101100110111001001011110100010010
    000000000000000000000000000000000000000000000000000000001000001 110011100100101110011010001000001110010111110010010111101011100
    000000000000000000000000000000000000000000000000000000000100000 011100111100101001100001001101010110111101101100000001110000010
    000000000000000000000000000000000000000000000000000000000010000 000110001010011110010000100011111010101110001000100000001111100
    000000000000000000000000000000000000000000000000000000000001001 110011100100101110011010001000001110010111110010010111101010100
    000000000000000000000000000000000000000000000000000000000000100 000110001010011110010000100011111010101110001000100000001111000
    000000000000000000000000000000000000000000000000000000000000010 000110001010011110010000100011111010101110001000100000001111010
    000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 100000000000000000000000000000000000000000000000000000000000000 010111101101001011111000101110110100110101011001110010101100100
    010000000000000000000000000000000000000000000000000000000000001 011011010011001011101001010100100101001110001110000101101110010
    001000000000000000000000000000000000000000000000000000000000000 100010001100111111000101111111011000011001000110111011001111100
    000100000000000000000000000000000000000000000000000000000000001 010110111001100111110000110110010111110000101010100001010010100
    000010000000000000000000000000000000000000000000000000000000001 001100000010011000000110101110110001011111001000000100011110100
    000001000000000000000000000000000000000000000000000000000000000 100111001011100101000110101010011100100001100100110010110000110
    000000100000000000000000000000000000000000000000000000000000001 100001001000000000000000100101101110110111001001111110110010010
    000000010000000000000000000000000000000000000000000000000000000 110111111111011101111101111000100000001110111100000110001000000
    000000001000000000000000000000000000000000000000000000000000000 110000101100101010101000111101100001010100101110101101010101000
    000000000100000000000000000000000000000000000000000000000000000 001011010000000101110100000000100100111111111100110111001111110
    000000000010000000000000000000000000000000000000000000000000000 010000010010100010010001011100110001111000100011101110000011100
    000000000001000000000000000000000000000000000000000000000000001 111111010011010110000111010000110111000110111101000111010011010
    000000000000100000000000000000000000000000000000000000000000000 100000011111011111100110111011000010010100110000001100111100100
    000000000000010000000000000000000000000000000000000000000000001 100110110100101100100111011101000100100111110010111011111000100
    000000000000001000000000000000000000000000000000000000000000001 110011100100101110011010001000001110011111110010011111100011100
    000000000000000100000000000000000000000000000000000000000000001 010010000111111111111100100110000000000001101011000001011111000
    000000000000000010000000000000000000000000000000000000000000000 101000100101001111001100011111110110010010001000101111001011000
    000000000000000001000000000000000000000000000000000000000000000 101000100010010011101111111111100001111110010000111010011110100
    000000000000000000100000000000000000000000000000000000000000001 001110101000001010010011010111101010100101010010110111001101100
    000000000000000000010000000000000000000000000000000000000000001 100100011010110000110010100100110000001010100001100111111000000
    000000000000000000001000000000000000000000000000000000000000001 101001101111001111000000001110100000100100010011111101101100100
    000000000000000000000100000000000000000000000000000000000000000 111000011110011100111110010001011010111010001000001010010101010
    000000000000000000000010000000000000000000000000000000000000000 011100111100101001100001001101010110111101001100000011110100010
    000000000000000000000001000000000000000000000000000000000000000 000101001011111011010010101101101100111111010110101110101110000
    000000000000000000000000100000000000000000000000000000000000000 111110011111110011001000001000101000110000010011101110100011100
    000000000000000000000000010000000000000000000000000000000000001 100001000001001001000011100001011110110000011101011111001001000
    000000000000000000000000001000000000000000000000000000000000000 101110000011001110001111100101101110100100101111101001101101010
    000000000000000000000000000100000000000000000000000000000000000 000111110110001000010110110001011000100001110010000101110111010
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    000000000000000000000000000001000000000000000000000000000000001 010100000010100001100000001001001010110000110011110110010111000
    000000000000000000000000000000100000000000000000000000000000000 000110001010011110010000100011111010101110001010100000101101100
    000000000000000000000000000000010000000000000000000000000000000 010111101101001011111000101110100100110101011001110010101100100
    000000000000000000000000000000001000000000000000000000000000000 100010001100111111000101111111010000011001000110111011001111100
    000000000000000000000000000000000100000000000000000000000000001 001100000010011000000110101110110101011111001000000100011110100
    000000000000000000000000000000000010000000000000000000000000001 100001001000000000000000100101101100110111001001111110110010010
    000000000000000000000000000000000001000000000000000000000000000 110000101100101010101000111101100000010100101110101101010101000
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Null basis vectors

nv0 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
nv0 = 0x00000000000000000000000000000001
nv0 = 1

See also: