On Helberg's Generalization of the Levenshtein Code for Multiple Deletion/Insertion Error Correction

A proof that the Helberg code is capable of correcting multiple deletion/insertion errors is presented. This code is a generalization of the number-theoretic Levenshtein code which is capable of correcting a single deletion/insertion. However, apart from exhaustive testing of short codes, no proof was hitherto given to verify that the Helberg code is indeed capable of correcting multiple deletions and insertions.