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

In this correspondence, for a positive integer M and a prime p such that M|pn - 1, three families of M-ary sequences using the M-ary Sidel'nikov sequences with period pn - 1 are constructed. Two small families contain [(pn - 1)/2]+M-2 or pn+M-3 M-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.