Comments on "A New Construction of 16-QAM Golay Complementary Sequences" and Extension for 64-QAM Golay Sequences

For original article by C.V. Chong see ibid. Vol.49, no.11, p.2953-2959, Nov. 2003. Some corrections are given for the sequence pairing descriptions of 16-QAM Golay complementary sequences in Chong, Venkataramani, and Tarokh´s paper, together with a related correction for Lee and Golomb´s 64-QAM Golay sequence construction. Lee and Golomb obtained 496, 808, and 976 offset pairs for length 2^m 64-QAM Golay sequences, m = 2,3,4. We obtained 724, 972, and 1224 offset pairs. Adding w = 1 to Case III in Lee and Golomb´s construction gives some additional offset pairs, others are new and exist for m ges 3 only. Descriptions of new offset pairs and enumeration for all first order offset pairs are proposed as conjectures. An example is given to show that there exist other 64-QAM Golay sequences not within this construction.