The detection of double errors in ISBN- and ISSN-like codes

Coding of the ISBN and ISSN is studied, and possible alternatives, not all equivalent to the official ones, are formulated. A minimum requirement for a useful code is that all single errors as well as all permutations of two symbols must be detectable. The strength of alternative codes, in particular with respect to the detection of double errors, is investigated. We give a complete description of the method based on division by 11 (the ISO norm). In this case, we are also able to describe the power of the method with respect to the detection of three or four errors. We show that, using division by 11, all coding methods detect the same percentage of errors. In case larger prime numbers are used as a divisor, numerical experiments were performed showing that different methods have different detection capabilities for double errors. The best methods are experimentally determined.