Talk:Hamming(7,4)

Split

I just split this from Hamming code so forgive me if parts of it read like it was from the other article. Cburnett 02:56, 2 January 2007 (UTC)

I overhauled the entire article and rewrote it to follow the general Hamming code form (parity bit $p_{k}$ on the $2^{k}$ bit). Cburnett 06:34, 2 January 2007 (UTC)

Question about the order of bits

What is the reason the bits are arranged in that order (for example in the first table in the 'Goal' section)? Wouldn't it make more sense to have the 4 data bits first? 93.172.144.97 (talk) 14:44, 6 July 2009 (UTC)

I agree, that should be explained early on 129.241.123.192 (talk) 20:58, 30 July 2009 (UTC)

Naming of the data vector

It is confusing that the data bits are named $d_{i}$ and the parity bits $p_{i}$, while the data vector is named $\mathbf {p}$. Is this a widespread convention? The data vector should ideally be named $\mathbf {d}$, or the naming of the bits should be changed. 129.241.123.192 (talk) 21:02, 30 July 2009 (UTC)

The generator matrix G

According to entry Hamming code,the generator matrix G of Hamming(7,4) shall be 4 by 7. But In Hamming(7,4), the G is 7 by 4. --Zxl.gzhu (talk) 07:58, 11 April 2010 (UTC)

Hamming(7,4) matrices G and H

These are different in this article and in Hamming code. Is at least one of these correct? Matma Rex pl.wiki talk 23:07, 24 March 2012 (UTC)

Describing the error-correcting capabilities

At present, the page says "Hamming's (7,4) algorithm can correct any single-bit error, or detect all single-bit and two-bit errors." I believe this is confusing, because it makes it sound like the code has two modes: (1) correcting single-bit errors, or (2) merely detecting single-bit errors as well as two-bit errors.

A subtlety is that the code can actually be used two ways, (1) correcting single-bit errors and detecting two-bit errors (but three-bit errors are "corrected" to an incorrect message), or (2) detecting all errors of up to three bits. This may not be an important thing to mention in the article, but it adds a level of confusion to the way it's currently written. — Preceding unsigned comment added by 141.222.21.196 (talk) 17:36, 15 July 2015 (UTC)

I don't think the above comment is correct. From my understanding, the (7, 4) Hamming code can operate in one of two modes: 1) it can correct all single-bit errors 2) it can detect all single-bit and two-bit errors. It can't do both at the same time, because a two-bit error looks like a single-bit error for a different message.

I agree that it should be clarified that there are two different incompatible modes. Kerrick Staley (talk) 20:03, 1 July 2022 (UTC)

G

G should be [I_4 | P] should it not? That's how it is in Cryptography with Coding Theory by Trappe. This G (transpose) is different? GalacticEncyclopedist (talk) 19:35, 22 November 2024 (UTC)