Combinatorial Characterizations of k-Coincidence Frequency-Hopping Sequences

Cao et al. characterize one-coincidence frequency-hopping (OC-FH) sequences in terms of perfect Mendelsohn packings (PMP). In this note, we generalize the definition of (v, n, lambda)-PMP to (k, v, n, lambda)-PMP and provide combinatorial characterizations for sets of k-coincidence frequency-hopping (k-FH) sequences interms of (k, v, n, lambda)-PMP. As a consequence, results on perfect Mendelsohn packings and perfect Mendelsohn designs can be used to construct such sets of k-FH sequences.