The Cross-Correlation of Binary Sequences With Optimal Autocorrelation

Binary sequences with low correlation have applications in communication systems and cryptography. Though binary sequences with optimal autocorrelation were constructed in the literature, no pair of binary sequences with optimal autocorrelation are known to have also best possible cross correlation. In this paper, new bounds on the cross correlation of binary sequences with optimal autocorrelation are derived, and pairs of binary sequences having optimal autocorrelation and meeting some of these bounds are presented. These new bounds are better than the Sarwate bounds on the cross correlation of binary sequences with optimal autocorrelation.