<p style='text-indent:20px;'>Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.</p>

中文翻译：

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关于 Welch 界和 Levenshtein 界的渐近最优码本的构造

<p style='text-indent:20px;'>码分多址通信系统中使用最大互相关幅度较小的码本来区分来自不同用户的信号。本文介绍了几类码本，其最大互相关幅值渐近达到相应的韦尔奇界和列文斯坦界。特别地，获得了关于 Levenshtein 界的一类最优码本。这些类型的码本是通过分别从循环矩阵、傅里叶矩阵和 Hadamard 矩阵中确定性地选择某些行来构建的。本文提供的部分码本的构造方法和参数是新的。</p>