I found multiple optimal CRC-32 polynomials on the CRC Polynomal Zoo site of Philip Koopman. Now I want to generate a CRC lookup table for one of the polynomials, by using the software pycrc.
To generate a CRC lookup table you have to provide the following information for the choosen polynomial:
For some polynomials I found the above parameters in a specification (for instance a AUTOSAR specification for the polynomial "F4ACFB13"), but what parameters should I choose if there is no specification for a certain polynomial? The Koopman site doesn't seem to provide the recommended parameters to use.
I already tried to find an explanation how to choose these parameters, but I could only find explanations how to implement these parameters and not how to choose them. Most websites recommend searching for specifications describing "common CRC polynomials", because they provide the optimal parameters.
Generally you are trying to match the CRC used in some existing protocol. In that case you need to do the same thing you did for the AUTOSAR CRC: find the specification for the CRC. Or you need to get several examples of messages and correct CRCs and try to reverse-engineer the CRC parameters.
You can find over a hundred CRC definitions here.
If you are creating your own protocol from scratch, then you can select any polynomial, reflection, initial value, and final exclusive-or you like, as well as any byte order of the CRC in the message. I would recommend that the polynomial be chosen with good properties for your message length from Phil's data, and that the initial value of the CRC register, init, not be zero. (If it is zero, then the CRC of any string of zeros will be the same value, that final exclusive-or, regardless of the length.) Also there is no detriment, and it is more aesthetic to pick the initial value and the final exclusive-or to be equal, so that the CRC of an empty sequence is zero.