  In this paper, using the theory of polynomial residue class rings, a new
construction is proposed for frequency hopping patterns having optimal Hamming
autocorrelation with respect to the well-known $Lempel$-$Greenberger$ bound.
Based on the proposed construction, many new $Peng$-$Fan$ optimal families of
frequency hopping sequences are obtained. The parameters of these sets of
frequency hopping sequences are new and flexible.
