If a gun is built as a handgun, and the barrel is rifled, there's no max or min barrel length required.
"The (Ithaca) Auto & Burglar Gun was a U.S.-made factory-built handgun that was commercially manufactured by configuring a standard double-barrel shotgun with a pistol grip, at first engraving and later stamping "Auto & Burglar Gun" on each side of the frame, and shortening the barrels to about 10" to 12.2" in length....
Ithaca stopped manufacturing the Auto & Burglar Gun when it became subject to registration and a $200 transfer tax under the National Firearms Act (NFA) of 1934 (the transfer tax was reduced to $5 in 1960). Relatively few Auto & Burglar Guns were manufactured, and they are today highly prized as collector's items....While it is sometimes incorrectly identified as a "sawed-off shotgun," the Ithaca Auto & Burglar Gun is a smooth bore pistol which since 1934 has been classified as an "Any Other Weapon" (AOW)[3] under the NFA, and it must be registered with the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF). Auto & Burglar Guns that are not currently registered are contraband, and cannot be legally possessed or registered. The penalties for illegal possession include up to a $250,000 fine and 10 years in prison."