Number of one-coincidence sequence sets for frequency-hopping multiple access communication systems

The paper presents a new and general description of a class of one-coincidence sequence sets. The set leaders of this class are derived from the combination of N linearly independent phases of a binary m-sequence of length S= 2N¿¿1. This class will be referred to in this paper as the m-sequence class of one-coincidence sequences. The total number of one-coincidence sets of this class is derived. It is shown that the total number of the m-sequence class of one-coincidence sets is much larger than the number previously described in the literature. A general proof of the one-coincidence property of these sets is presented, and four equivalent conditions for the existence of one-coincidence sequence sets is derived.