Frequency-hopping code sequence designs having large linear span

In frequency-hopping spread-spectrum multiple-access communication systems, it is desirable to use sets of hopping patterns that, in addition to having good Hamming correlation properties and large period, are also derived from sequences having large linear span. Here, two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented. The Hamming correlation properties of the designs are optimal in the first case and close to optimal in the second. In terms of the alphabet size p (required to be prime in both cases), the period and family size of the two designs are given by (p², p) and (p ⁿ, p^n/2+1) (n an even integer), respectively. The finite field sequences underlying the patterns in the first design have linear span exceeding p, whereas still larger linear spans (when compared to the sequence period) can be obtained using the second design method