论文标题
互补序列对的新结构超过$ 4^q $ -qam
New Constructions of Complementary Sequence Pairs over $4^q$-QAM
论文作者
论文摘要
正交振幅调节（QAM）GOLAY补充序列（GCSS）的先前结构被推广为$ 4^Q $ -QAM GCSS长度为$ 2^{m} $，通过li \ textsl {et al。}（et et al。}）（$ q \ g ge 2 $）的总体案例和liu} andive case nive case nive case nive case niv case。 2013年分别针对$ q \ ge 3 $）。这些序列作为第四纪标准GCS和兼容偏移的组合表示。通过基于整数$ Q $的分解提供新的兼容偏移，我们提出了两个新的构造为$ 4^Q $ -QAM GCSS，它们的概述I-V作为特殊情况。拟议的GCSS的数量（包括广义案例IV-V）等于第四纪标准GCSS数量和兼容偏移量的乘积。对于$ q = q = q_ {1} \ times q_ {2} \ times \ dots \ times q_ {t} $（$ q_k> 1 $），我们的第一个构造中的新换乘数量由$ m $ $ m $的多项式限制为$ $ t $ $ t $，而$ t $ $ $ $ $ y-i-iii a a和iii a a in a a in a in agiii and a line a in aiv and a in a in a in n off line and a line and a line and a line and a linial a和iii a aimiii a a in a”分别为$ m $的二次多项式。特别是，我们第一次建筑中的新偏移数量是$ q = 4 $的普遍案例IV-V的七倍。我们还表明，我们的两个结构中的新偏移数量被$ m $ $ q = 6 $的立方多项式限制。此外，我们的证明意味着本文中提到的所有QAM上提到的GCSS被视为Golay互补阵列的投影尺寸$ 2 \ times2 \ times2 \ times \ cdots \ times2 $。
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 \textsl{et al.} (the generalized cases I-III for $q\ge 2$) in 2010 and Liu \textsl{et al.} (the generalized cases IV-V for $q\ge 3$) in 2013 respectively. Those sequences are presented as the combination of the quaternary standard GCSs and compatible offsets. By providing new compatible offsets based on the factorization of the integer $q$, we proposed two new constructions of $4^q $-QAM GCSs, which have the generalized cases I-V as special cases. The numbers of the proposed GCSs (including the generalized cases IV-V) are equal to the product of the number of the quaternary standard GCSs and the number of the compatible offsets. For $q=q_{1}\times q_{2}\times \dots\times q_{t}$ ($q_k>1$), the number of new offsets in our first construction is lower bounded by a polynomial of $m$ with degree $t$, while the numbers of offsets in the generalized cases I-III and IV-V are a linear polynomial of $m$ and a quadratic polynomial of $m$, respectively. In particular, the numbers of new offsets in our first construction is seven times more than that in the generalized cases IV-V for $q=4$. We also show that the numbers of new offsets in our two constructions is lower bounded by a cubic polynomial of $m$ for $q=6$. Moreover, our proof implies that all the mentioned GCSs over QAM in this paper can be regarded as projections of Golay complementary arrays of size $2\times2\times\cdots\times2$.
