New Constructions of Even-Length Perfect Gaussian Integer Sequences

Perfect Gaussian integer sequences (PGISs) with ideal periodic autocorrelation functions have been extensively used to communication systems and cryptosystems. This paper propose several new families of even-length PGISs based on novel base sequences. The resulting sequences consists of at most 12 Gaussian integers. The new developed construction method is to use Gaussian integers of different Euclidean norms as the coefficients of a linear combination of the newly presented and previously developed base sequences. Both theoretical proofs and illustrated examples for new PGISs are given. The advantages of these new PGISs are either low energy or large degree when compared to the existing sequences.