Sorry but they do not exist in the NFA. A short barreled rifle has a barrel less than 16" and a stock.
Machine gun receivers are subject to the NFA for transfer, this is probably the reason for the confusion.
http://www.atf.gov/firearms/faq/nati...-shotguns.html
Q: What is the registered part of a Short Barreled Rifle (SBR) or Short Barreled Shotgun (SBS)?
A: While a receiver alone may be classified as a “firearm” under the Gun Control Act (GCA), SBRs and SBSs are classified in totality under the National Firearms Act (NFA).
A firearm that meets the definition of a SBR consists of a rifle that has a barrel less than 16 inches in length. A SBS consists of a shotgun that has a barrel less than 18 inches in length. The serialized receiver is recorded for registration in the National Firearms Registration and Transfer Record (NFRTR).
Q: I possess a properly registered SBR or SBS. I intend to strip the receiver and remove the barrel prior to selling the receiver. Is the bare receiver still subject to regulation under the NFA as a SBR or SBS?
A:
A stripped receiver without a barrel does not meet the definition of a SBR or SBS under the NFA. Although the previously registered firearm would remain registered unless the possessor notified the NFA Branch of the change, there is no provision in statute or regulation requiring registration of a firearm without a barrel because its physical characteristics would make it only a GCA “firearm” pursuant to 18 U.S.C. § 921(a)(3)(B). If the subsequent owner buys the receiver as a GCA firearm and installs a barrel less than 16 inches in length (SBR) or 18 inches in length (SBS), the firearm would be subject to a $200 making tax and registration under the NFA by the manufacturer or maker of the SBR or SBS. Because registration depends upon the stated intent of the applicant, there is no provision to allow registration of a NFA firearm by anyone other than the maker or manufacturer.