New Families of M-Ary Sequences With Low Correlation Constructed From Sidel'nikov Sequences

In this correspondence, for a positive integerMand a prime p such that M|pn- 1, three families of M-ary sequences using theM-ary Sidel'nikov sequences with period pn- 1 are constructed. Two small families contain [(pn- 1)/2]+M-2 or pn+M-3M-ary sequences, and both of their maximum magnitudes of correlation values are upper bounded by 2 radic{pn} + 6. The largest family has its maximum magnitude of correlation values upper bounded by 3 radic{pn}+5 and the family size is (M-1)2(2n-1-1) +M-1 for p = 2 or (M-1)2(pn- 3)/2 +M(M-1)/2 for an odd prime p.