Hey @idanP, this is a great write up! So far it is the most easy-to-read and in detail description of the maths behind the FRI protocol that I have seen. I very much like the fact that you provide all the mathematical background needed to understand Reed-Solomon Codes, including proofs of claims / lemmas, as well as giving out some exercises for all to do.

Some questions that I had after going through the post (though not fully in detail):

- How does the commitment scheme used in the commit phase affect the proving complexity? In other words, is the proof based on knowing all the pre-images to the values in the merkle tree? (Albeit, this may be out of scope for the FRI protocol)
- Where are the main points of possible efficiency improvements / optimizations?
- How does the soundness of the FRI protocol affect the overall zkSTARK construction? I understand that there is also the Fiat-Shamir soundness to keep into account

Thanks again for sharing this!