Optimal Sets of Frequency Hopping Sequences With Large Linear Spans

Frequency hopping (FH) is one of the basic spread coding technologies in spread spectrum communications. FH sequences are needed in FH code-division multiple access (CDMA) systems. For the anti-jamming purpose, FH sequences are required to have a large linear span. A few optimal sets of FH sequences are available in the literature. However, their sequences have very small linear spans. It is known that an optimal set of FH sequences could be transformed to another optimal set of FH sequences with large linear spans by a power permutation, if the power is chosen properly [see C. Ding and J. Yin, IEEE Trans. Inf. Theory, vol. IT-54, pp. 3741-3745, 2008]. The objective of this paper is to investigate this idea of C. Ding and J. Yin further, and determine the linear span of the FH sequences in the optimal sets obtained by applying a power permutation to some existing optimal sets of FH sequences.