CONTRACT: Clarify applicibility of wiki entry in Hamming contracts.

[gmcew]

closes #1610
Wording changes here are to emphasise the "extended" part of the contract structure. In parallel, there has been positive feedback on the 3b1b video's presence on discord, and I think the wiki entry still has some value in the very entry-level understanding of what a Hamming code is.

It's draft since I'd appreciate any comments/suggestions on collating further improvements to limit follow-on corrections.

[d0sboots]

Seems good to me. Probably marginally better, but these contracts will always have issues. (Fundamentally, the concepts are more complicated than the code here.)

[d0sboots]

I'm happy with this as is; comment or do something if you're happy to have it merged, otherwise I'll forget about it.

[bupjae]

An 'extended Hamming code' has an additional parity bit to enhance error detection and correction.

To be more precise, the additional parity bit of "extended" hamming code enhances the error detection when compared to plain hamming code, but not for correction.

• plain hamming code can detect and correct 1-bit error, but cannot detect 2-bit or more error.
• extended hamming code can still correct only 1-bit error, but able to detect up to 2-bit error. (so-called SECDED)

As our contract required to correct up to 1-bit error, this won't be affected for implementing solver. However, as we are trying to clarify the problem description, it would be good to be more precise.

[gmcew]

I'm happy with this as is; comment or do something if you're happy to have it merged, otherwise I'll forget about it.

Thanks, I'm happy to have it merged. I completely agree this is not likely to be the last revision of this description; it is a complex concept to distill down effectively.