Hamming distance

[WhiteCube]

I've been thinking about error correcting codes. Reed-Solomon in particular. The wikipedia article is a tough read, but I don't think the math needs to be so complicated.

If I'm using 10 bits, and I want to detect and correct 2 bit errors, I need to find codes that have a Hamming distance >4.

I did some random searches, and the best group of codes had 12 members.

Using that in the simplest way gives me 3 bits of data, and 7 non-data.

I don't know if 12 is the maximum, but my gut tells me there's a simple way to construct the codes. I hope so, because my random approach won't work for more bits.

 

[WhiteCube]

This is not going well at all. This might be a computationally hard problem.

I'll settle for limiting myself to 10 bits and proving 12 codes is the maximum.

I'm trying a backtracking search, but it is far too slow.

 

[WhiteCube]

A tricky subject.

Do you ever get the impression that people who write wikipedia articles are just explaining a subject to people who already understand it?

I'll stick to 7 bit Hamming codes, and let university students wrangle with 23 bit binary Golay codes.