The Autocorrelation Magnitude of Balanced Binary Sequence Pairs of Prime Period $N\equiv 1(\bmod\ 4)$ With Optimal Cross-Correlation.

In this paper, for balanced binary sequence pairs (BBSPs for short) of period $N\!\equiv\! 1(\bmod\, 4) $, the optimality of their cross-correlation is determined. Next, a lower bound on the maximal out-of-phase autocorrelation magnitude is established for BBSPs of period $N\!\equiv\! 1(\bmod\, 4) $ with optimal cross-correlation. Furthermore, BBSPs with optimal cross-correlation whose maximal out-of-phase autocorrelation magnitude achieves the new lower bound are constructed based on the cyclotomy of order 4. These proposed sequences have a periodic total squared correlation value meeting the Ganapathy-Pados-Karystinos bound, and are therefore an option for use in asynchronous CDMA systems. [ABSTRACT FROM PUBLISHER]