Hello, I know this is a very late reply but I've just found this forum when searching for for other info. I saw your question about this and you were correct in that 165810 was using AE04B0 but it was merely a miscode of one of the transponder boxes. 57-1419 KC-135 was always the correct user of this code.
165810 was transmitting both AE04A8 and AE04B0 at various times, so it looks as if one of the transponders has had the incorrect code set up.
To solve the mystery of what has happened to 165810, you can look here:
Getting back to the rogue transponder code, it can be quite common to see an incorrect code on older aircraft. I've had experience setting up these codes on [civil] aircraft and on older generation aircraft, it's not as simple as you might think. A lot of older generation aircraft the actual code is not generated in the transponder unit at all, it is generated by program pins on the aircraft wiring side, so once set-up any transponder plugged into that aircraft will automatically generate the correct code. Obviously, in this situation the actual hex code has to be converted into binary as the aircraft digital systems only actually work in binary [with normally a positive voltage being a "1" and a ground being a "0"] That binary figure then has to be transferred to wiring on the connector on the back on the transponder unit [normally a plug with many pins] so the potential for a coding error is quite high. That said, any decent engineer would always set up a ground test set after the installation had been done to check the hexcode outputs [on both systems].
This is also one of the reasons that aircraft when they change hands [and registrations] quite often fly around for a while with the code of the previous identity, as it's not a five minute job to recode on the older aircraft that are hard wired.