New families of asymptotically optimal codebooks from vectorial dual-bent functions

Yadi Wei; Jiaxin Wang; Fang-Wei Fu; Wenjuan Yin

New families of asymptotically optimal codebooks from vectorial dual-bent functions

Information Theory 2026-06-29 v1

Authors: Yadi Wei , Jiaxin Wang , Fang-Wei Fu , Wenjuan Yin

Abstract

Codebooks with small maximum cross-correlation amplitudes play an important role in many applications, such as code division multiple access (CDMA) communication systems, multiple-input multiple-output (MIMO) communications, compressed sensing, and coding theory. In this paper, by using vectorial dual-bent functions, we construct several families of codebooks that asymptotically achieve the Welch bound. The maximum cross-correlation amplitudes and the distributions of the cross-correlation amplitudes of the constructed codebooks are explicitly determined. Furthermore, these codebooks have new parameters, and some of them have very small alphabet sizes.

Keywords

codebooks vectorial dual-bent functions Welch bound cross-correlation amplitude CDMA MIMO communications

Cite

@article{arxiv.2606.29950,
  title  = {New families of asymptotically optimal codebooks from vectorial dual-bent functions},
  author = {Yadi Wei and Jiaxin Wang and Fang-Wei Fu and Wenjuan Yin},
  journal= {arXiv preprint arXiv:2606.29950},
  year   = {2026}
}