response 11 of 15:

Jan 25 18:46 UTC 2006

I don't believe it's a two-way communication stream; I believe that the 
remote only transmits and the opener only listens.

My semi-educated guess is that the remote transmits 2 things: a nonce,
and a code such that code = f_k(nonce) where k is the key which is
hard-coded into the remote.   Each time you press the button it uses a
different nonce, and so sends a different code.  The opener keeps track
of previously-used nonces (they may be strictly sequential or something)
so that replaying a previously used (nonce, code) combination won't open
the door a second time.