One-coincidence sequences with specified distance between adjacent symbols for frequency-hopping multiple access

Frequency hopping spread-spectrum systems have been popular in multiple-access communication systems. In such frequency-hopping multiple-access systems, multilevel sequences are used to specify which frequency will be used for transmission at any given time. One-coincidence sequences with specified distance between adjacent symbols for frequency-hopping multiple access are described. In such sequences, the distances between any adjacent symbols in any sequence are more than some specified amount. A theoretical bound is derived for the sequences, and two theorems on the construction of the sequences are given.