Wow, that's nasty... some of it has echos of reed-solomon, but that's all I can follow once it gets past defining conventional RAID in matrix terms.
I can tell you that this stuff is obscure. Really obscure. This isn't just your regular nasty math that any professor can figure out - this is cutting-edge research maths. There have only been a handful of papers I can find on the subject. There are probably about ten people who really understand this right now. It doesn't look impossible to follow, just arcane enough that even a professional mathematician is going to need to slog over it for an hour.
I can tell you the big catch though - and it's a really big catch. Failure model. These codes are made for correcting unreadable blocks on a hard drive, and depend upon the rest of that hard drive still being accessible. They won't do you a lot of good when two whole drives die at once. At least, that's as far as I can follow it. I'm not entirely confident, but I think that's how it works.
Might be applicable to flash controllers though - while drives tend to fail in a 'clunk-bzz-dead' manner, flash memory is more likely to lose individual cells.