Given a residue code representing a number N
with the tuple (N, R(N))
where R(N) equals N mod A
.
What is the error detection distance of a certain check base A
? In other words, how many bits can be flipped but still detect an error?
Edit:
I would think the minimum distance is 2 for any base. Consider a base A > 2. If N
equals 1, R(N) also equals 1. If we now look for for N+1 = 2, R(N) equals 2. The Hamming distance between those residue tuples is HD((1, 1), (2, 2)) = 2
, which cannot be better.