@article{Zhou2025, 
author = {Junchao Zhou and Tingting Pang},
title = {Two classes of nearly optimal codebooks from generalized bent              Z              4      -valued quadratic forms},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {24730-24754},
keywords = {codebook, Z4-valued quadratic form, generalized bent function, Boolean bent function, nearly optimal},
url = {https://www.sciopen.com/article/10.3934/math.20251096},
doi = {10.3934/math.20251096},
abstract = {Codebooks with small maximum cross-correlations are desirable in many fields, such as compressed sensing, direct spread code-division multiple-access (CDMA) systems, and space-time codes. The objective of this paper is the construction of codebooks. Based on the theory of              Z              4      -valued quadratic forms, we propose two classes of generalized bent functions over              Z              4      , and construct new families of codebooks from these functions. The codebooks obtained in this paper are nearly optimal with respect to the Welch bound, and could have a very small alphabet size, which is of importance in practical applications. Moreover, some Boolean bent functions are also derived.}
}