On the undetected error probability of triple-error-correcting BCH codes

The probability of undetected error P_u( epsilon ) for the primitive triple-error-correcting BCH codes of blocklength 2^m-1 used solely for error detection on a binary symmetric channel with crossover probability epsilon u( epsilon ) increases monotonically with epsilon . For even values of m, this is not necessarily true. However, for a fixed epsilon , as m increases, P_u( epsilon ) approaches 2^-p, where p is the number of parity bits. Similar characteristics are exhibited by the extended codes.