That doesn't answer the question. Who do you give the command authority for that decision? Who gets to say "we cannot contact the headquarters", which amounts to being able to launch the nuclear weapons? And obviously if you want them to be able to launch under those circumstances you have to give them any "launch codes" or what-have-you beforehand.
Yeah, I mentioned the letters of last resort, but while the letter will contain orders, the captain has sole launch authority, and it's difficult to imagine the system could work in a way that avoids that - whatever process you require the captain to follow, they could simply decide to follow that process as though the leadership were uncontactable.
I don't know what the actual procedure is; however like with Science Fiction and 'Self Destruct' codes I would think that a multi-agent auth challenge would be required.
The captain and some fixed number of executive officers. Possibly with redundancy for one or two crew being dead. The auth codes would cause a safe to unlock or message to de-crypt.
Presumably the instructions would be delivered to each authenticating member so that all could receive the orders simultaneously.
