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I took the opportunity to dabble with this. Interpreting the equations in the context of an implementation in software is tricky because there are many ways in which the polynomials can be mapped to data structures in memory - and, I assume, you'll want the solution you produce to seamlessly inter-operate with other implementations. In this context, it matters if your byte ordering is MSB or LSB first... it also matters if you align your bit-strings that aren't a multiple of 8 to the left or right. It is worth noting that the polynomials are denoted in ascending powers of X - whereas one might assume, because the leftmost bit in a byte has maximum index, that the leftmost bit should correspond to the maximum power of X - but that's not the convention in use. Essentially, there are two very different approaches to calculating CRCs using generator polynomials. The first, and least efficient, is to use arbitrary precision arithmetic and modulo - as the posted extract suggests. A faster approach involves successive application of the polynomial and exclusive-or. A implementation in Pascal can be found here: <a href="http://jetvision.de/sbs/adsb/crc.htm" rel="nofollow">http://jetvision.de/sbs/adsb/crc.htm</a> - translation to C# should prove trivial. A more direct approach might involve encoding the message and the generator polynomial as System.Numerics.BigInteger objects (using C#/.Net 4.0) and calculate the parity bits exactly as the text above suggests - by finding the message modulo the polynomial - simply using the "%" operator on suitably encoded BigIntegers. The only challenge here is in converting your message and parity bits to/from a format suitable for your application.
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