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Improved linear complexities of the frequency hopping sequences in two optimal sets

Gao J., Li X., Wei Y.

Control and Cybernetics

2012

Vol. 41, no. 2

317-334

For the anti-jamming purpose, high linear complexity is desired for each frequency hopping sequence in an optimal set. Using a proper power permutation, Wang has shown that an optimal set of frequency hopping sequences with small linear complexity can be transformed into a new optimal set of frequency hopping sequences with large linear complexity. This paper conains two results. First, we extend the result of Wang. A power permutation is only suitable for a special construction of optimal set of frequency hopping sequences, see Wang (2011). However, the power permutation chosen in this paper applies to the general construction of optimal set of frequency hopping sequences. Second, by using a binomial permutation polynomial P(x), which is different from those permutations used before, we obtain a novel optimal set of frequency hopping sequences with high linear complexity from an optimal set of frequency hopping sequences with small linear complexity. By counting the number of 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.