I thought I'd take a peek at the novelization of Star Trek: The Motion Picture
written by Gene Roddenberry himself. Folks may remember that as the movie opens, the V'Ger cloud attacks a bunch of Klingon ships. In the novelization, Kirk is actually able to "see" this happening. (An emergency signal was transmitted directly to an implant in Kirk's brain--a sort of emergency communication device.)
"Kirk found himself seeing three Klingon cruisers which appeared to be moving at warp velocity and in battle formation. The images became more detailed, increasingly real--he could begin thinking about them consciously. The Klingon vessels were big, dangerous looking--undoubtedly their new K't'inga
-class heavy cruisers which some Admiralty tacticians feared might prove faster and more powerful than Starfleet's First Line Constitution
I don't know what the secret is to their speed, but that advantage probably won't last. "Military secrets are the most fleeting of all."