In this paper, we show that if the d-decimation of a (q-1)-ary Sidelnikov sequence of period q-1=pm-1 is the d-multiple of the same Sidelnikov sequence, then d must be a power of a prime p. Also, we calculate the crosscorrelation magnitude between some constant multiples of d- and d'-decimations of a Sidelnikov sequence of period q-1 to be upper bounded by (d+d'-1)√q+3.

Let p be an odd prime such that p ≡ 3 mod 4 and n be an odd positive integer. In this paper, two new families of p-ary sequences of period $N = rac{p^n-1}{2}$ are constructed by two decimated p-ary m-sequences m(2t) and m(dt), where d=4 and d=(pn+1)/2=N+1. The upper bound on the magnitude of correlation values of two sequences in the family is derived by using Weil bound. Their upper bound is derived as $rac{3}{sqrt{2}} sqrt{N+rac{1}{2}}+rac{1}{2}$ and the family size is 4N, which is four times the period of the sequence.