In this letter, based on cyclic difference sets with parameters $(N,rac{N-1}{2},rac{N-3}{4})$ and complex transformations, a method for constructing degree-4 perfect Gaussian integer sequences (PGISs) with good balance property of length $N'equiv2( ext{mod}4)$ are presented. Furthermore, the elements distribution of the proposed Gaussian integer sequences (GISs) is derived.

Quadriphase sequences with good correlation properties are required in higher order digital modulation schemes, e.g., for timing measurements, channel estimation or synchronization. In this letter, based on interleaving technique and pairs of mismatched binary sequences with perfect cross-correlation function (PCCF), two new methods for constructing quadriphase sequences with mismatched filtering which exist for even length N ≡ 2(mod4) are presented. The resultant perfect mismatched quadriphase sequences have high energy efficiencies. Compared with the existing methods, the new methods have flexible parameters and can give cyclically distinct perfect mismatched quadriphase sequences.

In this letter, several new families of binary sequence pairs with period N=np, where p is a prime and gcd(n,p)=1, and optimal correlation values 1 and -3 are constructed. These classes of binary sequence pairs are based on Chinese remainder theorem. The constructed sequence pairs have optimum balance among 0's and 1's.