The probability of undetected error can have several local maxima
We show that for a code used for error detection in the binary-symmetric channel (BSC), the probability of an undetected error can have several local maxims, In particular, we construct a code with three local maxima in (0, 1/2), a code with five local maxims in (0, 1); and a linear code with two local maxima in (0, 1/2) and a linear code with three local maxima in (0, 1).
probability of undetected error error detection distance distribution error-detecting codes