A two-error-detecting arithmetical check system for decimal identification numbers

This paper proposes an arithmetical check computation, applicable to any decimal identification number consisting of at most twenty information digits. It first describes the check system for identification numbers of ten or less information digits; afterwards the paper generalizes the idea for identification numbers consisting of more than ten but less than twenty information digits. In respective cases the number or redundant check digits to be added is two or three, such that the information rate is ever about 85%. The computed check digits are capable of detecting the following types of errors which may possibly corrupt the identification number through the operating system: any single error, any double error, any combintion of one altered information digit and two interchanged information digits. It is asserted that this paper may be of practical interest to be taken into consideration whenever a new application involving identification numbers is set up.