On the Construction of Even-Length Perfect Gaussian Integer Sequences

The paper addresses the problem of constructing new even-length perfect Gaussian integer sequences (ELPGIS) with at least 9 nonzero complex numbers. The resulting ELPGISs are linear combinations of the previously known base sequences of period 2,4 and the newly proposed base sequences of period 8. When compared to the existing ELPGISs, there are more different Gaussian integers in a new ELPGIS. As the sequence length increases, at most four Gaussian integers increase their absolute values. The newly developed sequences bring a significant benefit on increasing the degree of freedom.