A coding theory approach to error control in redundant residue number systems. I. Theory and single error correction

A coding theory approach to error control in redundant residue number systems (RRNSs) is presented. The concepts of Hamming weight, minimum distance, weight distribution, and error detection and correction capabilities in redundant residue number systems are introduced. The necessary and sufficient conditions for the desired error control capability are derived from the minimum distance point of view. Closed-form expressions are derived for approximate weight distributions. Computationally efficient procedures are described for correcting single errors. A coding theory framework is developed for redundant residue number systems, and an efficient numerical procedure is derived for a single error correction