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

by blue_tiger30
Tags: code, corrects, detect, error, errors, hamming
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blue_tiger30
#1
May10-13, 07:05 PM
P: 29
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) ?
if not please let me how to get the answers
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mfb
#2
May11-13, 08:19 AM
Mentor
P: 11,888
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.
Bassalisk
#3
May11-13, 09:11 AM
P: 951
Hamming codes are class of codes that have [itex] (2^{m}-1, 2^{m}-m-1,3) [/itex] 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.

blue_tiger30
#4
May11-13, 10:00 AM
P: 29
Does a hamming code always corrects one error and detect 2 errors ?

sorry I meant is the minimum distance always 3 ?
Bassalisk
#5
May11-13, 12:34 PM
P: 951
Quote Quote by blue_tiger30 View Post
sorry I meant is the minimum distance always 3 ?
For class of Hamming codes, yes.


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