It is not clear whether North Korea really admitted that it had nuclear weapons or not. Some US officials might have interpreted North Korea's words literally, as in Kelly's trip to North Korea last October.

Until now, North Korea has suggested about its alleged nuclear program ambiguously in order to exact economic and diplomatic concessions from the US. It's also possible, however, North Korea really possesses nuclear weapons which haven't been tested. If North Korea has nuclear arms, it would be a nuclear bomb made from plutonium, allegedly produced in the early 90's, and using coarse initiating facilities, made through tens of high explosive tests. Experts on nuclear problems pointed out "Explosive nuclear bomb can be produced by doing high explosive tests repeatedly, without having a nuke test."

Therefore, the most important thing is to figure out whether North Korea had produced plutorium enough for nuclear weapons in the early 90's, and succeeded in developing initiating facilities for ultrafast plutonium fusion. The problem is that this is extremely difficult information to get.