We show that the non-trivial correlation of two properly chosen column sequences of length q-1 from the array structure of two Sidelnikov sequences of periods qe-1 and qd-1, respectively, is upper-bounded by $(2d-1)sqrt{q} + 1$, if $2leq e < d < rac{1}{2}(sqrt{q}-rac{2}{sqrt{q}}+1)$. Based on this, we propose a construction by combining properly chosen columns from arrays of size $(q-1) imes rac{q^e-1}{q-1}$ with e=2,3,...,d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.

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.