The probability of undetected error can have several local maxima
Iiro S. Honkala, Tero K Laihonen · IEEE Transactions on Information Theory · 1999
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 maxima. In particular, we construct a code with three local maxima in (0, 1/2), a code with five local maxima 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).