Ment
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I'm not sure, but it seems to me that a hash sum of this kind might work:
(-1)*(bit1) + 2*(bit2) - 3*(bit3) + 4*(bit4)
That is, examples of messages:
0000 (main part) 000 (hash sum)
0001 100
0010 101
0011 001
0100 010
1000 111
But I find it difficult to prove or disprove that this will work. At first glance, it seems that there are errors. However, it is possible that I simply overlooked a situation where this is not the case.