On the average hamming correlation of frequency-hopping sequence sets with good maximum hamming correlation

For frequency-hopping spread spectrum (FHSS) communication systems, the average Hamming correlation (AHC) among frequency-hopping sequences (FHSs) is an important performance measure, as well as the maximum Hamming correlation (MHC). In this paper, we study FHS sets with optimal AHC and good MHC. First, we analyze the AHC of known FHS sets with optimal MHC, and check their optimalities. We then prove the optimality of the AHC of perfectly balanced FHS sets and present some examples. Finally, we construct new FHS sets with optimal AHC by using the theory of cyclotomy.