Prove that for any positive integers m and n, the check digit code in Z n m
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Prove that for any positive integers m and n, the check digit code in Znm with check vector c = 1 = [1, 1, . . . , 1] will detect all single errors. (That is, prove that if vectors u and v in Znm differ in exactly one entry, Then c · u ≠ c · v .)
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