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Fast Generation of Perfect Gaussian Integer Sequences of Primitive Length

The different constructions of perfect Gaussian integer sequences (PGISs) have been extensively investigated in the recent literature. Those sequences have also been applied in a wide range of comb-spectrum code division multiple access as well as precoded orthogonal frequency-division multiplexing systems. This paper presents the long PGISs of primitive length based on the novel polynomial computations over finite fields. Such a polynomial can be expressed by the newly discovered exponent, which is less than the previously known Kasami exponent. This fact leads to the fast generation of long PGISs.