Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(3): 561-574

Online first article May 15, 2023      Printed May 31, 2023

https://doi.org/10.4134/BKMS.b210374

Copyright © The Korean Mathematical Society.

MacWilliams-type identities on vectorial Boolean functions with bent components and applications

Jong Yoon Hyun

Konkuk University, Glocal Campus

Abstract

In this paper, we focus on establishing the MacWilliams-type identities on vectorial Boolean functions with bent component functions. As their applications, we provide a bound for the non-existence of vectorial dual-bent functions with prescribed minimum degree, and several Gleason-type theorems are presented as well.

Keywords: Extended Walsh transform, vectorial Boolean function, vectorial dual-bent function, MacWilliams-type identity, Gleason-type theorem

MSC numbers: 94B05, 94B25, 94C10, 06E30

Supported by: This paper was supported by Konkuk University in 2020.

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