On Theory and in Residue Fast Algorithms for Error Correction Number System Product Codes

h this paper, we develop a coding theory approach to error control in residue number system product codes. Based on this coding theory framework, new computationally efficient algorithms are derived for correcting single errors, double errors, multiple errors, and simultaneously detecting multiple errors and additive overtlow. These algorithms reduce the computational complexity of previously known algorithms by at least an order of magnitude. In addition, it is worthwhile to mention here that all the literature published thus far deals almost exclusively with single error correction.

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