Error codes constructed in residue number systems with non-pairwise-prime moduli

Codes constructed in a Residue Number System (RNS) of moduli m//1, m//2,. . . , m//n are non-binary, arithmetic codes whose codewords are vectors where the ith component is m//i-valued (1 less than equivalent to i less than equivalent to n). A new class of codes in RNS is described, where redundancy is introduced by removing the constraint that the moduli of the RNS be pairwise prime. The error-detecting and correcting capabilities of such codes are discussed and a simple approach to error detection, localization and correction is presented. Although the codes under consideration are quite inefficient in some respects, it is shown that they may provide a wide coverage of random errors. A subclass of these codes is examined in more detail.