內容介紹：A Gaussian integer is a complex number whose real and imaginary parts are both integers. A Gaussian integer sequence is called perfect if it satisfies the ideal periodic auto-correlation functions. That is, let S=(s(0),s(1),...,s(N-1)) be a complex sequence of period N, where s(t)=u(t)+v(t)i for u(t),v(t), and i=. The complex sequence S is said to be a perfect Gaussian integer sequence if is nonzero for and is zero for any ,where denotes the conjugate of a complex number . Recently, the perfect Gaussian integer sequences have been widely used in modern wireless communication systems, such as code division multiple access and orthogonal frequency-division multiplexing systems. In this research, two different methods are presented to generate the long perfect Gaussian integer sequences with ideal periodic auto-correlation functions. The key idea of the proposed methods is to use a short perfect Gaussian integer sequence together with the polynomial or trace computation over an extension field to construct a family of the long perfect Gaussian integer sequences. The period of the resulting long sequences is not a multiple of that of the short sequence, which has not been investigated so far. Compared with the already existing methods, the proposed methods have three significant advantages that a single short perfect Gaussian integer sequence is employed, the long sequences consist of two distinct Gaussian integers, and their energy efficiency is monotone increasing.