If an aggressor launches a nuclear device of whatever size and detonates it above the atmosphere and in the line of site of its target country, the x-rays and gamma rays emitted by the blast will cause an electromagnetic pulse, or wave a million times stronger than the strongest radio wave.
Even the wave of sympathy that brought eager shoppers in from north and south of the border in the first Christmas after the blast has not been repeated in subsequent years - partly due to a rash of bomb hoaxes.