Correlation of Column Sequences from the Arrays of Sidelnikov Sequences of Different Periods

Abstract

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 q^e-1 and q^d-1, respectively, is upper-bounded by $(2d-1)\sqrt{q} + 1$, if $2\leq e < d < \frac{1}{2}(\sqrt{q}-\frac{2}{\sqrt{q}}+1)$. Based on this, we propose a construction by combining properly chosen columns from arrays of size $(q-1) \times \frac{q^e-1}{q-1}$ 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.