On the Construction of 64-QAM Golay Complementary Sequences

The construction of 64-QAM Golay sequences is discussed based on extensions of Lee and Golomb´s construction. On length n = 2^m sequences, Lee and Golomb reported 496, 808, and 976 first order offset pairs for m=2, 3, 4. We found 724, 972, and 1224 offset pairs from computer search over all first order offset pairs. Some additional pairs can be obtained by adding w = 1 to Case III in Lee and Golomb´s offset pair descriptions, others are new and only exist for w>3. The descriptions of new offset pairs and the enumeration of all first order offset pairs are proposed as conjectures. The number of first order offset pairs, [240(m + 1) + 4 + 2(m - 2)(m + 1)], agrees with computer results for ;m=2~6. The peak envelope power upper bound is shown to remain as 4.6667n. An example shows that other 64-QAM Golay sequences not within this construction can be generated using QPSK Golay sequences with third order algebraic normal form.