Nearly optimal codebooks from generalized Boolean bent functions over $ \mathbb{Z}_{4} $

Abstract

<p style='text-indent:20px;'>In this paper, based on the theory of <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_{4} $\end{document}</tex-math></inline-formula>-valued quadratic forms we propose several classes of generalized Boolean bent functions over <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{Z}_{4} $\end{document}</tex-math></inline-formula>, and new families of codebooks are constructed from these functions. The codebooks constructed in this paper are nearly optimal with respect to the Welch bound, and their parameters are new. Furthermore, some Boolean bent functions are also derived.</p>