Perfect Gaussian integer sequences from cyclic difference sets

A Gaussian integer is a complex number whose real and imaginary parts are both integers. This paper proposed a unified construction of perfect Gaussian integer sequences based on cyclic difference sets. It turns out that this construction produces an abundance of perfect Gaussian integer sequences. The proposed construction includes all the sequences recently given by Lee et. al as special cases, and many new families of Gaussian integer sequences. To illustrate, two classes of perfect Gaussian integer sequences defined from Kasami-Welch functions and Helleseth-Gong functions are given.