Verify 1100110 belongs to the (7, 4, 3) Hamming code

Question

I'm trying to verify 1100110 belongs to the (7, 4, 3) Hamming code. This means that there is length 7, dimension 4, and minimum distance 3. Obviously it has length 7. If it is one of three others in C, then dimension is satisfied, but I don't know how to verify that. And if no codeword is the same in more than four places, then distance is satisfied, but again not sure how to show that.

Answer 1

With the standard construction of the Hamming code, a word is in the code iff it has an even number of set bits in common with each of 1010101, 0110011, 0001111. This is the case for 1100110.

Remark. With a different convention, one could use test patterns 1010101, 1100110, 1111000 instead. That results in a different $(7,4,3)$ code (e.g., it does not contain 0001111). Incidentally, it does contain 1100110.