On the Cross-Correlation Distributions of $M$-ary Multiplicative Character Sequences
Yun Kyoung Han, Kyeongcheol Yang · IEEE Transactions on Information Theory · 2009
It is well known that the magnitude of the cross correlation between any distinct constant multiple sequences of anM-ary power residue sequence of periodpis upper bounded byradicp+2 and that of anM-ary Sidel'nikov sequence of periodpm-1 is upper bounded byradic{pm} +3, wherepis a prime andmis a positive integer. In this paper, we first show that their cross-correlation functions are closely related to Jacobi sums and cyclotomic numbers. We then derive the cross-correlation distribution of constant multiple sequences of anM-ary power residue sequence. In the case of constant multiple sequences of anM-ary Sidel'nikov sequence, we get the possible cross-correlation values whose occurrence numbers are expressed in terms of the cyclotomic numbers of orderMand are possibly zero.