[Bulat-Ziganshin]

among the great answers that was already written here, i can suggest famous Plank tutorial: https://web.eecs.utk.edu/~plank/plank/papers/CS-96-332.html

i (FastECC author) learned everything from this great text. It contains anything required to understand RS coding from standard programmer knowledge base (i.e no Galois Fields or matrix arithmetic). it's longer than most other texts referenced here but it contains enough info to even make your own implementation if you want

note that it doesn't include info regarding my fast O(N*logN) implementation. If you need to learn that - read docs in my repository, although i'm not as good teacher as professor Plank

also note that there are several different approaches to RS implementation. While they all are called RS codes, they are pretty different. Plank describes the scheme that is easier to understand (and implement) than any other one