On the Sidel'nikov Sequences as Frequency-Hopping Sequences
Yun Kyoung Han, Kyeongcheol Yang · IEEE Transactions on Information Theory · 2009
A(v,l, lambda)-FHS denotes a frequency-hopping sequence of lengthvover a frequency set of sizelwith maximum out-of-phase Hamming autocorrelationlambda. Recently, Ding and Yin constructed two FHS families for a prime powerqsatisfyingq=ef+1 with positive integerseandf. Theorems 4 and 5 in their paper claim that these two FHS families include optimal(q-1,e,f)-FHSs and(q-1,e+1,f-1)-FHSs with respect to the Lempel-Greenberger bound, respectively. In this paper, we give counterexamples and make corrections to them. Furthermore, we observe that these FHSs are closely related to Sidel'nikov sequences. Based on our results on the spectrum of their Hamming autocorrelation values, we also correct the theorem on the spectrum of Hamming distances of nearly equidistant codes derived by Sidel'nikov.