A new class of check-digit methods for arbitrary number systems (Corresp.)

For arbitrary number systems we present a new check-digit method that detects all single-digit errors and all transpositions of adjacent digits using a single check digit from the given number system. In previous methods at least one type of transpositional error had to remain undetected. The key to this method lies in using the dihedral groups together with appropriate transformations in the important cases, where the numbers are represented in base
2r
with
r
odd.