Detection and correction of multiple errors in general block codes

The paper deals with general block codes where the symbol sets at each coordinate do not have to be the same. First of all, the classical Hamming bound inequality for error correcting systems is extended to this case. a new necessary condition for systems able to detect all 1,…, 2k — 1-errors (k ∈ ℕ) is proved. From this a new bound for such systems is proved. All results are proved to be optimal. sults have applications, e.g., in ISBN (International Standard Book Number) or ISSN (International Standard Serial Number)-like systems.