gf(2) Find null basis vectors of M

M = 00000000000000000000000000000000000000000000000000000000000000
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    00000000000000000000000000000000000000000000000100000010000000
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    10110000111011110001101000010111010101000001110011011110100001
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    00110000110100110000000111101111100001011011100000000011010010
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    11010100100111000101010011100010000000000001000110001101100000
    01111000000100011100101110000111001010111000000001110101011001
Augment M with identity (I) of same size
M = 00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000001
    00000000000000000000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000000000000000000010100 00000000000000000000000000000000000000000000000000000000000100
    00000000000000000000000000000000000000000000000000000001001000 00000000000000000000000000000000000000000000000000000000001000
    00000000000000000000000000000000000000000000000000000100010000 00000000000000000000000000000000000000000000000000000000010000
    00000000000000000000000000000000000000000000000000010000100000 00000000000000000000000000000000000000000000000000000000100000
    00000000000000000000000000000000000000000000000001000001000000 00000000000000000000000000000000000000000000000000000001000000
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    00000000000000000000000100000000000000000010000000000000000000 00000000000000000000000000000000000000000010000000000000000000
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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 = 00010000000000000000000000000000000000000000000000000000000000001000010011010110010011011001000101100101110010001001010011100000
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    00000001000000000000000000000000000000000000000000000000000000011000101011101000001000011010001110111000100110001000110111101100
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    00000000000001000000000000000000000000000000000000000000000000000000110111001111110010010110000010000101110010011100111100111110
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    00000000000000001000000000000000000000000000000000000000000000011010010110101110111010100011010011111001110111011111100100010100
    00000000000000000100000000000000000000000000000000000000000000010010001100001101110101110010000110010011010010001110110001111000
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    00000000000000000001000000000000000000000000000000000000000000000010001110010010111000101110001001010110011101111001101100010100
    00000000000000000000100000000000000000000000000000000000000000000000100101000000000001111000101100110010010011110110001000101110
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    00000000000000000000001000000000000000000000000000000000000000010000001111110101000011111001110100000001001000111111101110011010
    00000000000000000000000100000000000000000000000000000000000000011010111101001010100100110010000101011111110111110111000110100000
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    00000000000000000000000000000000000000000000010000000000000000011010101001001110001101101100100110000011000100011000110000001000
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    00000000000000000000000000000000000000000000000100000000000000011010000110001000110001011001101110110010010011001111100101011100
    00000000000000000000000000000000000000000000000010000000000000010000000000000000000000000000000000000000000000000000000100010110
    00000000000000000000000000000000000000000000000001000000000000010000011010101111111010011100100100011000101000001100101100110100
    00000000000000000000000000000000000000000000000000100000000000011000110000110011100010100011011010011111100100100101101011101000
    00000000000000000000000000000000000000000000000000010000000000000010101101010001000000001001001000001100111001011110100011000010
    00000000000000000000000000000000000000000000000000001000000000011010010110101110111010100011010011111000110111011110100100010100
    00000000000000000000000000000000000000000000000000000100000000000000100101000000000001111000101100110010000011110110101000101110
    00000000000000000000000000000000000000000000000000000010000000011010000110011010011000000001100001001000100011100011011010110100
    00000000000000000000000000000000000000000000000000000001000000011010010000100010010001001011101100001000011101100110100111101100
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    00000000000000000000000000000000000000000000000000000000010000011000110000110011100010100011011010011111100100100101101001101000
    00000000000000000000000000000000000000000000000000000000001000011010010110101110111010100011010011111000110111011110100101010100
    00000000000000000000000000000000000000000000000000000000000100011010000110011010011000000001100001001000100011100011011010010100
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    00000000000000000000000000000000000000000000000000000000000001011010010110101110111010100011010011111000110111011110100101011100
    00000000000000000000000000000000000000000000000000000000000000110000000000000000000000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000000000000000000000000000001001001110000010000101110001001010001010011001000101011011100
    00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
M in augmented form
M = 10000000000000000000000000000000000000000000000000000000000001 00010011010110010011011001000101100101110010001001010011100000
    01000000000000000000000000000000000000000000000000000000000010 00011010101111111010011100100101011000101000000100101100110100
    00100000000000000000000000000000000000000000000000000000000001 00010111001111011110000000111000001001010111100010000110011110
    00010000000000000000000000000000000000000000000000000000000001 00111111100001100111111000001010101101111100110000011001100010
    00001000000000000000000000000000000000000000000000000000000011 00101011101000001000011010001110111000100110001000110111101100
    00000100000000000000000000000000000000000000000000000000000011 00110000110011100010100011011010001111100100100001101011101000
    00000010000000000000000000000000000000000000000000000000000010 00000010011001010110001101010110110111000010010001100100111000
    00000001000000000000000000000000000000000000000000000000000000 10000000001011100000011000010001010010100100110111010010000100
    00000000100000000000000000000000000000000000000000000000000010 00011100000110000111000110101110010010100000110000010101110100
    00000000010000000000000000000000000000000000000000000000000000 10101101010001000000001001001000001000111001011100100011000010
    00000000001000000000000000000000000000000000000000000000000000 00110111001111110010010110000010000101110010011100111100111110
    00000000000100000000000000000000000000000000000000000000000010 00110011011110001111101101110011000001011001110100111111111000
    00000000000010000000000000000000000000000000000000000000000011 00101111101101011010011100111000010110001101111111000000001100
    00000000000001000000000000000000000000000000000000000000000011 10010110101110111010100011010011111001110111011111100100010100
    00000000000000100000000000000000000000000000000000000000000010 10001100001101110101110010000110010011010010001110110001111000
    00000000000000010000000000000000000000000000000000000000000001 00111110111110110101100010011111101010110001001100111000001000
    00000000000000001000000000000000000000000000000000000000000000 10001110010010111000101110001001010110011101111001101100010100
    00000000000000000100000000000000000000000000000000000000000000 00100101000000000001111000101100110010010011110110001000101110
    00000000000000000010000000000000000000000000000000000000000000 00011000010001011001100000001101001101000110100001001001100010
    00000000000000000001000000000000000000000000000000000000000010 00001111110101000011111001110100000001001000111111101110011010
    00000000000000000000100000000000000000000000000000000000000011 10111101001010100100110010000101011111110111110111000110100000
    00000000000000000000010000000000000000000000000000000000000011 10000110011010011000000001100001001000100111100011001010110100
    00000000000000000000001000000000000000000000000000000000000001 10011011110001101110101111100001111000111001010000111000010010
    00000000000000000000000100000000000000000000000000000000000011 10101001001110001101101100100110000011000110011000110000001000
    00000000000000000000000010000000000000000000000000000000000010 10111101011010000010111001011000000011011110101101111001110110
    00000000000000000000000001000000000000000000000000000000000011 10010000100010010001001011101100001000011100100110101111101100
    00000000000000000000000000100000000000000000000000000000000001 00010000110000010001100001110111010111100000110101110000100110
    00000000000000000000000000010000000000000000000000000000000011 10000110001000110001011001101110110010010011101111100101011100
    00000000000000000000000000001000000000000000000000000000000010 10001001001111000010110010000110101111010000110100010001000010
    00000000000000000000000000000100000000000000000000000000000010 00000000000000000000000000000000000000000000010000000100010110
    00000000000000000000000000000010000000000000000000000000000001 10000101110001001100111111010101110110000101100010011101010110
    00000000000000000000000000000001000000000000000000000000000010 00011010101111111010011100100100011000101000000100101100110100
    00000000000000000000000000000000100000000000000000000000000001 00111111100001100111111000001010001101111100110000011001100010
    00000000000000000000000000000000010000000000000000000000000011 00110000110011100010100011011010011111100100100001101011101000
    00000000000000000000000000000000001000000000000000000000000000 10000000001011100000011000010001011010100100110111010010000100
    00000000000000000000000000000000000100000000000000000000000000 10101101010001000000001001001000001100111001011100100011000010
    00000000000000000000000000000000000010000000000000000000000010 00110011011110001111101101110011000011011001110100111111111000
    00000000000000000000000000000000000001000000000000000000000011 10010110101110111010100011010011111000110111011111100100010100
    00000000000000000000000000000000000000100000000000000000000001 00111110111110110101100010011111101010010001001100111000001000
    00000000000000000000000000000000000000010000000000000000000000 00100101000000000001111000101100110010000011110110001000101110
    00000000000000000000000000000000000000001000000000000000000010 00001111110101000011111001110100000001000000111111101110011010
    00000000000000000000000000000000000000000100000000000000000011 10000110011010011000000001100001001000100011100011001010110100
    00000000000000000000000000000000000000000010000000000000000011 10101001001110001101101100100110000011000100011000110000001000
    00000000000000000000000000000000000000000001000000000000000011 10010000100010010001001011101100001000011101100110101111101100
    00000000000000000000000000000000000000000000100000000000000011 10000110001000110001011001101110110010010011001111100101011100
    00000000000000000000000000000000000000000000010000000000000010 00000000000000000000000000000000000000000000000000000100010110
    00000000000000000000000000000000000000000000001000000000000010 00011010101111111010011100100100011000101000001100101100110100
    00000000000000000000000000000000000000000000000100000000000011 00110000110011100010100011011010011111100100100101101011101000
    00000000000000000000000000000000000000000000000010000000000000 10101101010001000000001001001000001100111001011110100011000010
    00000000000000000000000000000000000000000000000001000000000011 10010110101110111010100011010011111000110111011110100100010100
    00000000000000000000000000000000000000000000000000100000000000 00100101000000000001111000101100110010000011110110101000101110
    00000000000000000000000000000000000000000000000000010000000011 10000110011010011000000001100001001000100011100011011010110100
    00000000000000000000000000000000000000000000000000001000000011 10010000100010010001001011101100001000011101100110100111101100
    00000000000000000000000000000000000000000000000000000100000010 00000000000000000000000000000000000000000000000000000000010110
    00000000000000000000000000000000000000000000000000000010000011 00110000110011100010100011011010011111100100100101101001101000
    00000000000000000000000000000000000000000000000000000001000011 10010110101110111010100011010011111000110111011110100101010100
    00000000000000000000000000000000000000000000000000000000100011 10000110011010011000000001100001001000100011100011011010010100
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    00000000000000000000000000000000000000000000000000000000001011 10010110101110111010100011010011111000110111011110100101011100
    00000000000000000000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000000000000000000000000 01001001110000010000101110001001010001010011001000101011011100
    00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000001
Highlight null basis vectors (where left side of row is zero)
M = 10000000000000000000000000000000000000000000000000000000000001 00010011010110010011011001000101100101110010001001010011100000
    01000000000000000000000000000000000000000000000000000000000010 00011010101111111010011100100101011000101000000100101100110100
    00100000000000000000000000000000000000000000000000000000000001 00010111001111011110000000111000001001010111100010000110011110
    00010000000000000000000000000000000000000000000000000000000001 00111111100001100111111000001010101101111100110000011001100010
    00001000000000000000000000000000000000000000000000000000000011 00101011101000001000011010001110111000100110001000110111101100
    00000100000000000000000000000000000000000000000000000000000011 00110000110011100010100011011010001111100100100001101011101000
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    00000001000000000000000000000000000000000000000000000000000000 10000000001011100000011000010001010010100100110111010010000100
    00000000100000000000000000000000000000000000000000000000000010 00011100000110000111000110101110010010100000110000010101110100
    00000000010000000000000000000000000000000000000000000000000000 10101101010001000000001001001000001000111001011100100011000010
    00000000001000000000000000000000000000000000000000000000000000 00110111001111110010010110000010000101110010011100111100111110
    00000000000100000000000000000000000000000000000000000000000010 00110011011110001111101101110011000001011001110100111111111000
    00000000000010000000000000000000000000000000000000000000000011 00101111101101011010011100111000010110001101111111000000001100
    00000000000001000000000000000000000000000000000000000000000011 10010110101110111010100011010011111001110111011111100100010100
    00000000000000100000000000000000000000000000000000000000000010 10001100001101110101110010000110010011010010001110110001111000
    00000000000000010000000000000000000000000000000000000000000001 00111110111110110101100010011111101010110001001100111000001000
    00000000000000001000000000000000000000000000000000000000000000 10001110010010111000101110001001010110011101111001101100010100
    00000000000000000100000000000000000000000000000000000000000000 00100101000000000001111000101100110010010011110110001000101110
    00000000000000000010000000000000000000000000000000000000000000 00011000010001011001100000001101001101000110100001001001100010
    00000000000000000001000000000000000000000000000000000000000010 00001111110101000011111001110100000001001000111111101110011010
    00000000000000000000100000000000000000000000000000000000000011 10111101001010100100110010000101011111110111110111000110100000
    00000000000000000000010000000000000000000000000000000000000011 10000110011010011000000001100001001000100111100011001010110100
    00000000000000000000001000000000000000000000000000000000000001 10011011110001101110101111100001111000111001010000111000010010
    00000000000000000000000100000000000000000000000000000000000011 10101001001110001101101100100110000011000110011000110000001000
    00000000000000000000000010000000000000000000000000000000000010 10111101011010000010111001011000000011011110101101111001110110
    00000000000000000000000001000000000000000000000000000000000011 10010000100010010001001011101100001000011100100110101111101100
    00000000000000000000000000100000000000000000000000000000000001 00010000110000010001100001110111010111100000110101110000100110
    00000000000000000000000000010000000000000000000000000000000011 10000110001000110001011001101110110010010011101111100101011100
    00000000000000000000000000001000000000000000000000000000000010 10001001001111000010110010000110101111010000110100010001000010
    00000000000000000000000000000100000000000000000000000000000010 00000000000000000000000000000000000000000000010000000100010110
    00000000000000000000000000000010000000000000000000000000000001 10000101110001001100111111010101110110000101100010011101010110
    00000000000000000000000000000001000000000000000000000000000010 00011010101111111010011100100100011000101000000100101100110100
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    00000000000000000000000000000000000000000010000000000000000011 10101001001110001101101100100110000011000100011000110000001000
    00000000000000000000000000000000000000000001000000000000000011 10010000100010010001001011101100001000011101100110101111101100
    00000000000000000000000000000000000000000000100000000000000011 10000110001000110001011001101110110010010011001111100101011100
    00000000000000000000000000000000000000000000010000000000000010 00000000000000000000000000000000000000000000000000000100010110
    00000000000000000000000000000000000000000000001000000000000010 00011010101111111010011100100100011000101000001100101100110100
    00000000000000000000000000000000000000000000000100000000000011 00110000110011100010100011011010011111100100100101101011101000
    00000000000000000000000000000000000000000000000010000000000000 10101101010001000000001001001000001100111001011110100011000010
    00000000000000000000000000000000000000000000000001000000000011 10010110101110111010100011010011111000110111011110100100010100
    00000000000000000000000000000000000000000000000000100000000000 00100101000000000001111000101100110010000011110110101000101110
    00000000000000000000000000000000000000000000000000010000000011 10000110011010011000000001100001001000100011100011011010110100
    00000000000000000000000000000000000000000000000000001000000011 10010000100010010001001011101100001000011101100110100111101100
    00000000000000000000000000000000000000000000000000000100000010 00000000000000000000000000000000000000000000000000000000010110
    00000000000000000000000000000000000000000000000000000010000011 00110000110011100010100011011010011111100100100101101001101000
    00000000000000000000000000000000000000000000000000000001000011 10010110101110111010100011010011111000110111011110100101010100
    00000000000000000000000000000000000000000000000000000000100011 10000110011010011000000001100001001000100011100011011010010100
    00000000000000000000000000000000000000000000000000000000010010 00000000000000000000000000000000000000000000000000000000000110
    00000000000000000000000000000000000000000000000000000000001011 10010110101110111010100011010011111000110111011110100101011100
    00000000000000000000000000000000000000000000000000000000000110 00000000000000000000000000000000000000000000000000000000000010
    00000000000000000000000000000000000000000000000000000000000000 01001001110000010000101110001001010001010011001000101011011100
    00000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000001
Null basis vectors

nv0 = b0001001001110000010000101110001001010001010011001000101011011100
nv0 = 0x127042e2514c8adc
nv0 = x60 + x57 + x54 + x53 + x52 + x46 + x41 + x39 + x38 + x37 + x33 + x30 + x28 + x24 + x22 + x19 + x18 + x15 + x11 + x9 + x7 + x6 + x4 + x3 + x2

nv1 = b0000000000000000000000000000000000000000000000000000000000000001
nv1 = 0x0000000000000001
nv1 = 1

See also: