Does a hamming code always corrects one error and detect 2 errors ?

1. May 10, 2013

blue_tiger30

does a hamming code always corrects one error and detect 2 errors ? and is the distance always 3 ?
I know that that is true for (7,4) hamming code but does that apply to a (11,7) or (15,11) ?

2. May 11, 2013

Staff: Mentor

I think the Hamming distance of 3 is used for the definition of "Hamming code". You can use codes with more additional bits to get more error detection/correction, but (7,4), (15,11) and so on are always 2 bits detection / 1 bit correction.

3. May 11, 2013

Bassalisk

Hamming codes are class of codes that have $(2^{m}-1, 2^{m}-m-1,3)$ which means that they all correct one and only one error. I don't know about detection of those other two, I am not familiar with that. But the distance of 3 dictates that they can correct only one error.

4. May 11, 2013

blue_tiger30

sorry I meant is the minimum distance always 3 ?

5. May 11, 2013

Bassalisk

For class of Hamming codes, yes.