In this work, a coding theory approach to error control in redundant residue number systems is presented. We introduce the concepts of Hamming weight, minimum distance, weight distribution, and error detection and correction capabilities in redundant residue number systems. 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. Finally, computationally efficient procedures are described for correcting single errors. This paper is in two parts. In Part I, a coding theory framework is developed for redundant residue number systems, and an efficient numerical procedure is derived for a single error correction. Part I1 will deal with the extension of this framework and algorithms for correcting multiple errors and simultaneous error correction and detection.

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