what does this code mean? p1626 theft deterrent fuel signal

its says something like fuel signal not enable or something what is this and will this hurt gas mileage and i also have a bank 1 sensor 1 o2 sensor bad.

the theft deterrent system shuts off the fuel system should someone hotwire your car, or use a key that doesn't have the passkey chip in it. Shouldn't affect your gas mileage, but if you live in an area where your car could be stolen, I'd have it looked at.