I have a background in error codes - hamming, and luby and raptor and, and, and. Reed-Solomon is particularly "beautiful" from a mathematics perspective (more so than Raptor) - something I can usually explain to anyone and get them interested.
Do you want to give it a try? I just attempted to explain RS in https://news.ycombinator.com/item?id=19248444 but I am significantly impeded by the fact that I don't actually understand it myself, so I'm sort of summarizing the Wikipedia article. Am I focusing on the right algorithms? Did I explain them correctly, as far as my short explanation goes?
The explanation from BackBlaze that you linked to goes into more depth.
It looks to be built on matrix algebra.
Kinda nifty how simple and elegant the underlying concept is, really. Reminds me of the surprising conceptual simplicity behind Diffie-Hellman.
I guess simple is relative, but in my opinion, coding theory is not simple. It requires some high level math to understand what is going on. Many people's eyes will glaze over when you go into Galois (finite) fields. Abstract algebra is not part of the typical undegrad CS/engineering math curriculum. And then the efficient algorithms for the decoding procedure were found much later than Reed & Solomon's original paper by Berlekamp.
> Abstract algebra is not part of the typical undegrad CS/engineering math curriculum.
It should be (says the mathematician)! That it doesn't probably comes from confusing the elegant theoretical perspective on finite fields to the computational perspective, which (at least from my pure-math point of view) can get pretty hairy.
if you want to learn finite fields somewhat more formally, but not so formally, this is a pretty good introduction (yes, it's for AES, but the principles are the same): https://www.youtube.com/watch?v=x1v2tX4_dkQ
