New Constructions of Complementary Sequence Pairs over 4^q-QAM
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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 IV-V for q> 3) in 2013 respectively. Those sequences are represented as the weighted sum of q quaternary standard GCSs. In this paper, we present two new constructions for 4^q-QAM GCSs of length 2^m, where the proposed sequences are also represented as the weighted sum of q quaternary standard GCSs. It is shown that the generalized cases I-V are special cases of these two constructions. In particular, 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 example, in the case q=4, the number of new GCSs is seven times more than those in the generalized cases IV-V. In the case q=6, the ratio of the number of new GCSs and the generalized cases IV-V is greater than six and will increase in proportion with m. Moreover, our proof implies all the mentioned GCSs over QAM in this paper can be regarded as projections of Golay complementary arrays of size 2×2×...×2.
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