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.

Nice. There are quite a few implementations of R-S floating around out there

I'll plug mine, too, written in C. https://github.com/quiet/libcorrect

Learning enough about finite fields to implement one is really mind bending. Definitely recommend people try it, or at least make the encoder side

Fun mathematical aside: if you have a polynomial with positive integral coefficients, then you can uniquely determine it with only two points, no matter the degree.

An explanation of Reed-Solomon ECC decoding, using field arithmetic and linear algebra, with runnable code: https://www.nayuki.io/page/reed-solomon-error-correcting-cod...

> Your MP3 maybe got knocked down, but it got up again. You’d need to lose more than 4 pieces to keep it down.

Nice

  high-performance [...] Reed-Solomon

Just had to say that this is probably the best explanation of Reed-Solomon I've seen: practical explanations, useful visuals, good pacing, just enough humor. :)

fun stuff. wrote once a decoder from reading data tracks from cd in raw mode :)

what's the percentage overhead based on the initial stream? i.e. 10%, 20%?