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

Min Kyu SONG  Hong-Yeop SONG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E102-A   No.10   pp.1333-1339
Publication Date: 2019/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E102.A.1333
Type of Manuscript: PAPER
Category: Coding Theory
Sidelnikov sequences,  array structure,  correlation,  

Full Text: FreePDF(955KB)

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.