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

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

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arXiv · 2606.29950

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

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

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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.

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Yadi Wei, Jiaxin Wang, Fang-Wei Fu, Wenjuan Yin. 2026-06-29. New families of asymptotically optimal codebooks from vectorial dual-bent functions. https://arxiv.org/abs/2606.29950

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