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 2m - 1 used solely for error detection on a binary symmetric channel with cross-over probability epsilon less-than-or-equal-to 1/2 is examined. It is shown that for odd values of m, P(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.