🚀 go-pugleaf

In all the literature I've encountered on the Cyclic Redundancy Check, proofs
of its effectiveness have not discussed the length of the data being checked.
The proofs generally run something like so: if there is a single-bit error,
then blah blah, and if there is a double bit error then ..., and if there is
an odd number of bit errors ..., and if there is an error burst less than the
length of the checking polynomial then ..., and if there is an error burst
equal in length to the checking polynomial then ..., etc.  But it seems to me
that the longer the data, the more likely there will be (for instance) several
error bursts, in different places, and there is some chance that these errors
will cancel each other out in the CRC.  Does the probability that this will
happen increase with the length of the data, given a certain average bit error
rate?  And this leads to the question, is there an optimum message length for
a given checking polynomial and error rate?  Obviously, the longer the
message, the more efficient the use of the medium provided retransmissions can
be kept to a minimum...