An $ (N,K) $ codebook $ {\mathcal C} $ is a collection of $ N $ unit norm vectors in a $ K $-dimensional vectors space. In applications of codebooks such as CDMA, those vectors in a codebook should have a small maximum magnitude of inner products between any pair of distinct code vectors. In this paper, we propose two constructions of codebooks based on $ p $-ary linear codes and on a hybrid character sum of a special kind of functions, respectively. With these constructions, two classes of codebooks asymptotically meeting the Welch bound are presented.

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关于Welch界的两类近乎最佳的代码本

$（N，K）$码本$ {\ mathcal C} $是$ K $维向量空间中$ N $单位范式向量的集合。在诸如CDMA之类的密码本的应用中，密码本中的那些矢量在任何一对不同的代码矢量之间应具有很小的最大内积。在本文中，我们提出了两种基于$ p $ ary线性编码和特殊功能的混合字符和的码本结构。通过这些构造，提出了两类渐近满足Welch界线的密码本。