It may take more than a serial number to identify this canoe. The Old Town and the Carleton with this number are both 16 feet long (while the Kennebec is 17 feet). My guess is that you will find the Old Town based on the shipping location.
The Old Town canoe with serial number 19928 is a 16 foot long, CS (common sense or middle) grade, Charles River model with red western cedar planking, closed spruce gunwales, ash decks, ash thwarts, ash seats, and a keel. It was built between December, 1911 and March, 1912. The original exterior paint color was dark green. It shipped on April 30th, 1912 to Columbus, Ohio.
The Carleton canoe with serial number 19928 is a 16 foot long, regular (or middle) grade, Carleton model with red western cedar planking, open spruce gunwales, a keel and sponsons. It was built between November, 1929 and June, 1930. The original exterior paint color was dark red. It shipped on June 13th, 1930 to Wolfeboro, New Hampshire.
Scans of these build records can be found by following the links at the attached thumbnail images below. These scans and several hundred thousand others were created with substantial grants from the Wooden Canoe Heritage Association (WCHA) and others as you probably know well. A description of the project to preserve these records is available at
http://www.wcha.org/ot_records/ if you want more details. I hope that you will join or renew your membership to the WCHA so that services like this can continue. See
http://www.wcha.org/about-the-wcha/ to learn more about the WCHA and
http://store.wcha.org/WCHA-New-Membership.html to join.
It is also possible that you could find another number or manufacturer if these descriptions don't match the canoe. Feel free to reply here if you have any other questions.
Benson