The Zip Code Bar Code

I was recently asked by a chemist to figure out the scheme used to create the bar code for the extended zip code on business reply mail. With a half dozen samples to experiment with, this puzzle took a few hours to solve. Not unexpectedly, the code is an interesting application of modular arithmetic and a form of binary representation. This problem could be done in a high school or college class or used as a class project or a challenge problem for better students. It could also serve as a nice introduction to error-correcting codes.