Actually BB is a simple one. Basically each designation is started with a first letter denoting its class, F for Frigate, D for Destroyer, C for Cruiser, B for Battleship etcetera. And then a second letter follows to further define its role. If the letter repeats itself it means that its just a normal ship. so BB is battleship, CC is cruiser, and DD is destroyer.
But the extensions are stuff like
H for Heavy, L for Light, A for attack, assault , E for escort, G for guided missile etcetera.
So DH is heavy destroyer, CL is light Cruiser, FEG is an escort frigate with guided munitions, CVH is a heavy carrier, etcetera. Looking at my reference it seems that CA is

Attack Cruiser, but in my experience CA usually means Heavy Cruiser as I don't recall ever seeing a CH. There's also a few exceptions to the rule like:
DN - Dreadnought
BC - Battlecruiser (under normal schemes BC would be a mean a cargo-carrying Battleship)
If you check out this page:
http://www.datasync.com/~mtg02/ you can find all of the ship designation crap. On the left hand bar go to "Procedures" (second from the bottom) and then in the frame click on "Ship Designations"
Note - if the guy really wants "strike carrier" the proper designation would be CVA it seems. Though if I were him I'd just do CV as from experience, 'strike' always seems silly. If he wants something imposing, CVH (Heavy Carrier) sounds more brutish.
Further Note - Interestingly enough, under 'special' designations J is added for command or flagships, so CCJ is a command Cruiser. Given Freespace's shorter code (GTC instead of GTCC) Volition may have unintentionally given the Sathanas a Command ship code if you look at it as a designation rather than an abbreviation (SJ could be Shivan Command ship instead of Shivan Juggernaut).