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

2026-06-29

AI Summary

This work addresses the demand for low mutual-correlation codebooks in applications such as CDMA, MIMO communications, and compressed sensing by proposing a novel construction based on vectorial dual-bent functions. By integrating algebraic structures over finite fields with combinatorial design techniques, the authors construct, for the first time, multiple families of asymptotically optimal codebooks with new parameters whose maximum cross-correlation magnitudes approach the Welch bound. Notably, certain constructed codebooks achieve asymptotic optimality while significantly reducing alphabet size, thereby substantially expanding the parameter space beyond existing constructions.

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.

Problem

• codebooks
• cross-correlation
• Welch bound
• vectorial dual-bent functions
• asymptotically optimal

Innovation

• vectorial dual-bent functions
• asymptotically optimal codebooks
• Welch bound
• cross-correlation amplitude
• small alphabet size