A semi-related question/puzzle. Is it possible to reverse engineer parameters of a Reed Solomoon function?

Given one or more known inputs/outputs of a Reed Solomon function with known symbol size, message length, number of parity symbols. Is it possible to calculate the other parameters (polynomial coefficients, primitive element etc)?

I failed to find an answer a few years ago, when trying to interoperate with chirp.io (now gone). https://math.stackexchange.com/questions/663643/discover-par...