First some theory:
A Hamming code is defined for numbers [n,k] where and . Every k bits are encoded into n-bit codewords. Furthermore, every codeword in a Hamming code has a distance of minimum 3 to another codeword, which gives the ability of correcting 1 corrupt bit in each codeword (corrects 1 error per n-bits)
Having that said, please consider the [5,2] code (a non Hamming code, as per definition above). Every 2 bits are encoded into a 5 bit codeword, i.e.
This code have the exact characteristics, as far as I can see, as the Hamming code - the distance between codewords is minimum 3, and it corrects 1 error in 5 bits.
How come, then, that it is not classified as a Hamming code? Is there any difference that I have missed?