Error detection in decimal numbers

The code described detects those errors people most frequently make when transmitting decimal numbers. N digit numbers are encoded by appending a check digit determined by a computation involving the N digits. N + 1 digit numbers are "checked" by another computation. If an N digit number is encoded, and then any single digit is altered or any adjacent pair of digits is interchanged, the "check" computation will detect the error. A possible application: X-rays in hospitals are often indexed by patient number. Physicians request X-rays by number. Errors are discovered only when the plate is pulled and found to correspond to the wrong patient. By then the requester may no longer be available to supply the correct number. If numbers were encoded, most errors would be detected at the time the request was made.