LAUSR

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. This letter presents two different methods 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.