Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms compared with the linear block codes. The objective of this letter is to present a new family of ternary cyclic codes with parameters [3m-1,3m-1-2m,4], where m is an odd integer. The proposed cyclic codes are optimal in the sense that their parameters meet the Sphere Packing bound.

In this paper, a new class of low-hit-zone (LHZ) frequency-hopping sequence sets (LHZ FHS sets) is constructed based upon the Cartesian product, and the periodic partial Hamming correlation within its LHZ are studied. Studies have shown that the new LHZ FHS sets are optimal according to the periodic partial Hamming correlation bounds of FHS set, and some known FHS sets are the special cases of this new construction.

In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. But aperiodic Hamming correlation of FH sequences matters in real applications, while it received little attraction in the literature compared with periodic Hamming correlation. In this paper, the new aperiodic Hamming correlation lower bounds for FH sequences, with respect to the size of the frequency slot set, the sequence length, the family size, the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation are established. The new aperiodic bounds are tighter than the Peng-Fan bounds. In addition, the new bounds include the second powers of the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation but the Peng-Fan bounds do not include them. For the given sequence length, the family size and the frequency slot set size, the values of the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation are inside of an ellipse which is given by the new aperiodic bounds.

In this paper, new design of optimal frequency hopping sequences (FHSs) with low hit zone (LHZ) with respect to the Peng-Fan-Lee bound is presented based on interleaving techniques. By the new design, new classes of optimal LHZ FHS sets with large family size are obtained. It is shown that all the sequences in the proposed FHS sets are shift distinct. The proposed FHS sets are suitable for quasi-synchronous time/frequency hopping code division multiple access systems to eliminate multiple-access interference.

The construction of frequency hopping sequences with good Hamming correlation is the foundation of research in frequency hopping communication. In this letter, classes of optimal low hit zone frequency hopping sequence set are constructed based on the interleaving technology. The results of the study show that the sequence set with large family size is optimal for the Peng-Fan-Lee bound. And all the sequences in the set are inequivalent.

For an odd prime p, two new families of p-ary sequences of period pn-1 are constructed for odd n = 2l+1=(2m+1)e and even n = 2l = 2me, respectively. It is shown that, for a given integer ρ with 1 ≤ ρ ≤ m, the proposed sequence families both have maximum correlation magnitude , family size (pn-1)p(ρ-1)n+1, and maximum linear span .

The frequency hopping sequence plays a crucial role in determining the system's anti-jamming performance, in frequency hopping communication systems. If the adjacent frequency points of FHS can ensure wide-gap, it will better improve the anti-interference capability of the FH communication system. Moreover, if the period of the sequence is expanded, and each frequency point does not repeat in the same sequence, the system's ability to resist electromagnetic interference will be enhanced. And a one-coincidence frequency-hopping sequence set consists of FHSs with maximum Hamming autocorrelation 0 and cross-correlation 1. In this paper, we present two constructions of wide-gap frequency-hopping sequence sets. One construction is a new class of wide-gap one-coincidence FHS set, and the other is a WGFHS set with long period. These two WGFHS sets are optimal with respect to WG-Peng-Fan bound. And each sequence of these WGFHS sets is optimal with respect to WG-Lempel-Greenberger bound.

In order to evaluate the goodness of frequency hopping sequence design, the aperiodic Hamming correlation function is used as an important measure. In this letter, the aperiodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone which have not yet been reported previously are established.

In order to evaluate the goodness of frequency hopping sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen frequency hopping sequence, so the study of the partial Hamming correlation of frequency hopping sequence is particularly important. In this paper, the maximum partial Hamming correlation lower bounds of frequency hopping sequences with low hit zone, with respect to the size of the frequency slot set, the length of correlation window, the family size, the low hit zone, the maximum partial Hamming autocorrelation and the maximum partial Hamming crosscorrelation are established. It is shown that the new bounds include the known Lempel-Greenberger bound, Peng-Fan bounds, Eun-Jin-Hong-Song bound and Peng-Fan-Lee bounds as special cases.

In this paper, with a modification of our earlier construction in [12], new classes of optimal LHZ FHS sets with new parameters are obtained which are optimal in the sense that their parameters meet the Peng-Fan-Lee bound. It is shown that all the sequences in the proposed FHS sets are shift distinct. The proposed FHS sets are suitable for quasi-synchronous time/frequency hopping code division multiple access systems to eliminate multiple-access interference.