Balanced Quaternary Sequences Pairs of Odd Period With (Almost) Optimal Autocorrelation and Cross-Correlation

In this letter, two lower bounds on the maximum cross-correlation magnitude of balanced quaternary sequence pairs with (almost) optimal autocorrelation are presented. The maximum cross-correlation magnitude of a balanced quaternary sequence pair of period N with the maximum out-of-phase autocorrelation magnitude √5, where N = 4f + 1 is a prime and f is an odd integer, is shown to be √N, achieving one of the new lower bounds.