No nontrivial optimal sets of frequency-hopping sequences (FHSs) of period 2(2n-1) for a positive integer n ≥ 2 have been found so far, when their frequency set sizes are less than their periods. In this paper, systematic doubling methods to construct new FHS sets are presented under the constraint that the set of frequencies has size less than or equal to 2n. First, optimal FHS sets with respect to the Peng-Fan bound are constructed when frequency set size is either 2n-1 or 2n. And then, near-optimal FHS sets with frequency set size 2n-1 are designed by applying the Chinese Remainder Theorem to Sidel'nikov sequences, whose FHSs are optimal with respect to the Lempel-Greenberger bound. Finally, a general construction is given for near-optimal FHS sets whose frequency set size is less than 2n-1. Our constructions give new parameters not covered in the literature, which are summarized in Table1.

In this paper we present a construction method for quaternary sequences from a binary sequence of even period, which preserves the period and autocorrelation of the given binary sequence. By applying the method to the binary sequences with three-valued autocorrelation, we construct new quaternary sequences with three-valued autocorrelation, which are balanced or almost balanced. In particular, we construct new balanced quaternary sequences whose autocorrelations are three-valued and have out-of-phase magnitude 2, when their periods are N=pm-1 and N≡ 2 (mod 4) for any odd prime p and any odd integer m. Their out-of-phase autocorrelation magnitude is the known optimal value for N≠ 2,4,8, and 16.

In this letter, we enumerate the number of cyclically inequivalent M-ary Sidel'nikov sequences of given length as well as the number of distinct autocorrelation distributions that they can have, while we change the primitive element for generating the sequence.