Linear Complexities of the Frequency Hopping Sequences in Two Optimal Sets

For the secure purpose, large linear complexity is desired for each frequency hopping sequence in an optimal set. This paper gives two results. Firstly, we extend a result given by Wang. In [17], a power permutation is only suitable for a special construction of optimal set of frequency hopping sequences. However, the power permutation chosen in this paper applies to the general construction of optimal set of frequency hopping sequences. Secondly, by using a binomial permutation polynomial P(x), we obtain a novel optimal set of frequency hopping sequences with large linear complexity from an optimal set of frequency hopping sequences with small linear complexity. By counting the number of the different roots in the sequence representation, we determine the linear complexities of the frequency hopping sequences in two optimal sets transformed by the power permutation or binomial permutation.