Cant Figure Out Odd CRC

[iso9001]

Hi. :?

I'm working on a bus very similar to J1850 that is used in domestic cars. I'm having a problem figuring out just what exactly is going on with the CRC.... I cant find instances of this polynomial anywhere:

X^8 + X^4 + X^3 + X^2 + 1

So none of the google hits and whatnot have helped so far. I have the polynomial and the value that each equation must equall to be valid:

X^7 + X^6 + X^2 (C4 hex)

As well as some examples of valid bytes and thier CRC:

Data Bytes (hex) CRC (hex)
00 00 00 00 = 59
F2 01 83 = 37
0F AA 00 55 = 79
00 FF 55 11 = B8
33 22 55 AA BB CC DD EE FF = C8
92 6B 55 = 8C
FF FF FF FF = 74

What I dont know is how to derive them... Am I supposed to Mod 2 divide the message by the crc byte and expect the answer of C4 ???

Anyone ?

 

[monttyle]

[edited lots]

I studied CRC's in my communications class, and CRC's have a pretty funny definition of 'divide'. It's long-division done in binary, but instead of binary subtractions in each stage it's binary exclusive-or. Explaining in detail would mean quoting from the book since I don't have the details memorized, so instead I'd reccomend you take a look at "Understanding Data Communications & Networks" by William A. Shay, 2nd ed, ISBN 0-534-95054-X. Really cool book.