A New Construction of QAM Golay Complementary Sequence Pair

The previous constructions of quadrature amplitude modulation (QAM) Golay complementary sequences (GCSs) were generalized as 4(q)-QAM GCSs of length 2(m) by Li (the generalized cases I -III for q >= 2) in 2010 and Liu (the generalized cases IVV for q >= 3) in 2013 respectively. Those sequences are given by the weighted sum of q quaternary standard GCSs, which is represented as q -dimensional vectorial generalized Boolean functions (V-GBFs). In this paper, we present a new construction for 4q-QAM GCSs of length 2m. The new construction includes the generalized cases I -III as special cases. If q is a composite number, a great number of new GCSs other than the sequences in the generalized cases I -V will arise. For the cases q = 4 and q = 6, we show that the ratios of the number of new GCSs and the generalized cases I -V are greater than seven and six respectively if m is large enough.