Arithmetic codes in residue number systems

Residue number systems provide a means of constructing non-binary, multiple error correcting, arithmetic codes. A lower bound to redundancy allowing t-error correction in these codes is reported. It is shown that this bound is reached by two classes of codes, whose properties are discussed in detail. In both cases, error correction is performed by finding appropriate solutions to a key congruence, identical for both cases. Two different decoding algorithms and examples are reported.