Generic Construction of Binary Sequences of Period $2N$ With Optimal Odd Correlation Magnitude Based on Quaternary Sequences of Odd Period $N$

Abstract

Binary sequences with low odd correlation have important applications in communication systems to reduce interference. In this paper, using the interleaving technique, we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation. As a result, some new binary sequences with optimal odd auto-correlation magnitude are obtained. Besides, two sets consisting of $2^{n}+1$ binary sequences of period $2(2^{n}-1)$ with the maximum odd correlation magnitude $2^{((n+1)/ 2)}+2$ are derived, which are the first two optimal classes of binary sequence sets achieving the Sarwate bound on the odd correlation magnitude in the literature.