A frequency-hopping sequence (FHS) of length  v  and frequency set size  M  is called a  (v , M ,?)-FHS if its maximum out-of-phase Hamming autocorrelation is  ? . Three new classes of optimal FHSs with respect to the Lempel-Greenberger bound are presented in this paper. First, new optimal (p,M,f)-FHSs are constructed when p = Mf +1 is an odd prime such that  f  is even and p ? 3 mod 4 . And then, a construction for optimal (kp,p,k)-FHSs is given for any odd prime p and a positive integer K  1 ,p 1 (p 1  + 2 ),2 m  -1,or p 1   m -1, where p 1  and p 1 +2 are odd primes. Finally, several new optimal FHSs with maximum out-of-phase Hamming autocorrelation 1 or 2 are also presented. In particular, the existence of optimal (v,N,1)-FHSs is proven for any integer N ? 3 and any integer v with N +1 ? v ? 2 N-1, as well as the existence of optimal (2N +1,N,2)-FHSs is shown for any integer N ? 3. These classes of optimal FHSs have new parameters which are not covered in the literature.
['Jin-Ho Chung', 'Kyeongcheol Yang']
Optimal Frequency-Hopping Sequences With New Parameters