Okie has it right.
16 inch minimum length for rifle barrels, 18 inch minimum length for shotgun barrels, both have a minimum overall length requirement, as well, which i believe is 26 inches.
You can get any barrel length below that that you wish, but that requires a $200 tax stamp to register your weapon as a Short Barreled Rifle (or Shotgun).
An 18 inch barreled shotgun is an excellent home defense tool, i opted for the 20 inch, personally--5+1 or 7+1 and only adds an inch and a half.