I forgot to mention a crucial piece of information why De Bruijn sequences couldn't possibly work against Genie. The packet the remote sends is made of a 4-bit

I forgot to mention a crucial piece of information why De Bruijn sequences couldn't possibly work against Genie. The packet the remote sends is made of a 4-bit header followed by the 12-bit code, but the header is using a bit encoding (sequence of 10 and 20 kHz pulses) that couldn't possible represent a valid sequence of 0s and 1s in the code. So yeah, unless you can trick a Genie receiver to parse a code without the header, De Bruijn sequences can't work.