The author addresses a multiple header detection issue for the centralised spread-spectrum packet radio system with common directsequence/ binary phase-shift-keying (DS/BPSK) modulation. Chernoff bounds on the false alarm and missed detection probabilities of the header are derived and computed for a specific class of spreading codes and header sequences. Using these performance bounds, the author compares the header sequences and finds a good one which can be received with small probability of false alarm and high probability of correct detection. He also determines a proper randomisation time to minimise the two bounds for given system parameters, and then calculates the allowable number of transmitting radios subject to a constraint on the bounds for this randomisation time.