Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in CDMA communication systems. In this paper, we first study the Jacobi sums over Galois rings of arbitrary characteristics and completely determine their absolute values, which extends the work in [34], where the Jacobi sums over Galois rings with characteristics of a square of a prime number were discussed. Then, the deterministic construction of codebooks based on the Jacobi sums over Galois rings of arbitrary characteristics is presented, which produces asymptotically optimal codebooks with respect to the Welch bound. In addition, the parameters of the codebooks provided in this paper are new.

翻译：在本文中,我们首先研究在Galois环上任意性特征的Jacobi总和,并完全确定其绝对值,从而在[34] 中扩展了工作,其中讨论了在Galois环上进行的Jacobi总和,具有一个正方形的特性。然后,介绍了基于Jacobi总和的代码手册的决定性结构,它以具有任意性特征的Galois环上Jacobi总和为基础,产生了与Welch捆绑有关的非现式最佳代码手册。此外,本文件提供的代码手册参数是新的。