New families of M-ary sequences with low correlation constructed from Sidel'nikov sequences

Abstract

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