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I have a binary code $001011100000101100110$ which has a mistake and using Hamming Code. I need to fix this binary code and solve which hidden word is in this $001011100000101100110$.

Position $1$ checks $1,3,5,7,9,11,13,15,17,19,21$
Position $2$ checks $2,3,6,7,10,11,14,15,18,19$
Position $4$ checks $4,5,6,7,12,13,14,15,20,21$
Position $8$ checks $8,9,10,11,12,13,14,15$
Position $16$ checks $16,17,18,19,20,21$

I found an error in the main digits, namely in the second and sixteenth, and I can not decode the word

Trajan
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user434841
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    Presumably this is a shortened $[21, 16]$ nonsystematic Hamming code, shortened from the standard $[31,26]$ Hamming code. The code cannot correct two errors, and if you found that the 2nd and 16th bits are in error (How did you determine this? by the way), there is most likely a single bit error that will produce the same syndrome. – Dilip Sarwate May 21 '21 at 18:24
  • Repeating the comment from here: you haven't told us which Hamming code is used. Presumably Dilip got it right, and the bits are in standard order. Are what you call Position 1,2,4,8,16 to be the rows of a parity check matrix? – Jyrki Lahtonen May 25 '21 at 17:18

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