Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented.

中文翻译：

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几乎满足韦尔奇界限的新密码本结构

在许多领域，例如直接扩展码分多址通信、压缩感知等，都需要满足 Welch 等式约束的最优码本。然而，构建这样的最优码本是困难的。已经有许多尝试构建几乎满足韦尔奇界限的密码本。在本文中，我们使用从 [Formula: see text] 到 [Formula: see text] 的广义弯曲函数来介绍码本的通用构造，其中 [Formula: see text] 是素数， [Formula: see text] 是正数[公式：见正文]的整数。通过这种结构，我们获得了两个几乎符合 Welch 界限的新密码本系列。这些密码本具有新参数，并且可能具有较小的字母大小。特别是从[公式：见正文]到[公式：