White did use serial numbers briefly from the late 1940s until the early 1960s when Bub King was running the shop. The format was xx-yy-zzzz where xx was the length in feet, yy was the last two digits of the year, and zzzz was the sequential serial number. Hovever, there are no known White records to verify any of this.
This implies that your friend's canoe is 16 feet long and came off of the form in 1952. It was issued serial number 1588. Feel free to reply here if this doesn't answer your question.