I should have mentioned (and have now updated my original post to include) the target of the algorithm is a microcontroller with very limited RAM & Flash. Large lookup tables are out of the question.
As far as LFSRs being "undecodeable", read through the postings in the referenced link. I believe knowing the taps of the encode LFSR and the initial seed, there should be a (maybe not so trivial) mathematical algorithm that would decode the encoded bits.
Mind you, I also believe in Santa, and that global warming is a myth.
;-)