An Optimal Frequency Hopping Sequence Set Based on the Polynomial Theory

A new class of cubic frequency hopping (FH) sequence set is proposed in this paper. The new cubic FH sequence set is proved to be optimal with respect to the average Hamming correlation bound. Furthermore an optimal FH sequence set based on polynomial theory that is optimal with respect to the Singleton bound on FH sequences is also constructed. In addition, the average Hamming correlation of the optimal polynomial frequency hopping sequence set is discussed in this paper. The analysis result shows that the new polynomial FH sequence set is also optimal with respect to the average Hamming correlation bound.