Doesn’t seem too hard actually, given enough example input. The parity is just a linear combination of the input so you can set up a linear system and solve for those things encoding matrix rows pretty easily. From there you may need to make some assumptions about what type of matrix was used (e.g. vandermonde is popular) and perhaps the field size being used (e.g. GF(2^8), and with those, it should be easy to determine the reducing polynomial. Some of these choices are small enough to be able to brute force (finite fields used for practical problems tend to be small, naturally). If you have a dataset, I might actually toy with it myself.. sounds fun.
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Doesn’t seem too hard actually, given enough example input. The parity is just a linear combination of the input so you can set up a linear system and solve for those things encoding matrix rows pretty easily. From there you may need to make some assumptions about what type of matrix was used (e.g. vandermonde is popular) and perhaps the field size being used (e.g. GF(2^8), and with those, it should be easy to determine the reducing polynomial. Some of these choices are small enough to be able to brute force (finite fields used for practical problems tend to be small, naturally). If you have a dataset, I might actually toy with it myself.. sounds fun.
Thanks. I have 30 examples I got from the API, many moons ago https://github.com/moreati/chirppy/blob/master/examples.json. My finite field knowledge is not up to solving it analytically, my attempts to brute force it are in https://github.com/moreati/chirppy/blob/master/trials.py. That includes functions to go between the characters, and integer representations.