Golay Complementary Sequences Over the QAM Constellation.

Abstract. In this paper,we present new constructions for M2-QAM and 2M Q-PAM Golay complementary sequences of length 2n for inte-ger n, where M = 2m for integer m. New decision conditions are pro-posed to judge whether the sequences with offset pairs proposed by Ying Li are Golay complementary, and with the new decision conditions, we prove the conjecture 1 and point out some drawbacks in conjecture 2 proposed by Ying Li. We describe a new offset pairs and construct new 64-QAM Golay sequences based on this new offset pairs. We also study the 128-QAM Golay complementary sequences, and propose a new de-cision condition to judge whether the sequences are 128-QAM Golay complementary.