Fun to read, well written, but I am not a big fan of the "oversampling" based explanation, as you start to think about functions on real values that way, while it is really finite field maths that underpins the working of these codes.
Also, Reed Solomon is not a particularly great forward error correcting code. They are optimal as "erasure codes" (i.e, you can lose some data, but the remaining data cannot have changed), but as error correcting codes, LDPC codes / Turbo codes outperform them a lot: e.g. satellite communication (DVB-S2), hard drive error correction all switched to LDPC's.