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 (2^n-1-1) + M-1 for p = 2 or (M-1)²(pⁿ - 3)/2 + M(M-1)/2 for an odd prime p.