Parameterization of high-dimensional perfect sequences over a composition algebra over ℝ
Parameterization of high-dimensional perfect sequences over a composition algebra over ℝ
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DOI：
10.1587/transfun.e98.a.2439
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发表时间：
2015-12
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影响因子：
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通讯作者：
T. Maeda;Takafumi Hayashi
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文献类型：
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作者：
T. Maeda;Takafumi Hayashi
为了分析环上复合代数上的高维完全序列的结构，我们发展了这类序列的傅立叶变换理论。类似于离散傅立叶变换（DFT）的变换被引入一组序列。我们定义了离散余弦变换，离散正弦变换，广义离散傅立叶变换（GDFT）的序列，我们证明了这些变换的基本性质。我们证明了GDFT是双射的，并且这些变换和序列卷积之间存在关系。通过将这些性质应用于一组完全序列，我们得到了这组序列的参数化定理。利用这个定理，我们证明了左完全性和右完全性的等价性。
To analyze the structure of a set of high-dimensional perfect sequences over a composition algebra over ℝ, we developed the theory of Fourier transforms of such sequences. Transforms that are similar to discrete Fourier transforms (DFTs) are introduced for a set of sequences. We define the discrete cosine transform, the discrete sine transform, and the generalized discrete Fourier transform (GDFT) of the sequences, and we prove the fundamental properties of these transforms. We show that the GDFT is bijective and that there exists a relationship between these transforms and a convolution of sequences. By applying these properties to a set of perfect sequences, we obtain a parameterization theorem for the sequences. Using this theorem, we show the equivalence of the left and right perfectness.