Chinese Remaindering with Errors

The Chinese Remainder Theorem states that a positive integer m is uniquely speci ed by its remainder modulo k relatively prime integers p1;:::;pk, provided m < Qk i=1 pi. Thus the residues of m modulo relatively prime integers p1 < p2 < < pn form a redundant representation of m if m < Qk i=1 pi and k < n. This gives a number-theoretic construction of an \error-correcting code" that has been considered often in the past (see 41, 19, 35]). In this code a \message" (integer) m < Qk i=1 pi is encoded by the list of its residues modulu p1;:::;pn. By the Chinese Remainder Theorem, if a code-word is corrupted in e < n k 2 coordinates, then there exists a unique integer m whose corresponding code-word di ers from the corrupted word in at most e places. Furthermore, Mandelbaum 25, 26] shows how m can be recovered e ciently given the corrupted word, provided that the pi's are very close to one another. To deal with arbitrary pi's, we present a variant...

• Type: Journal
• Year: 1998
• Where: ECCC
• Authors: Oded Goldreich, Dana Ron, Madhu Sudan
• Keywords: Chinese Remainder Theorem, ECCC 1998, Qk I=1 Pi, Relatively Prime