Error Detecting Schemes Using Dihedral Groups

With inexpensive, fast, and reliable scanning devices and computers, it is now standard practice to append a check digit to product identification numbers, to detect errors and forgery. Various schemes for determining the checkdigit have been devised; we will refer to them interchangeably as schemes, methods, and codes. Surprisingly, schemes in use today vary greatly in their effectiveness in detecting (and correcting) errors.