On constructions and properties of self-dual generalized bent functions

2021/07/28 by A. V. Kutsenko, Kutsenko, Aleksandr
Computer Science · Engineering · Medicine · #94A60 #94D10 #Cancer Mechanisms and Therapy #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2107.13538

openalex publication_date 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bent functions of the form \mathbbF₂ⁿ→ℤ_q, where q\geqslant2 is a positive integer, are known as generalized bent (gbent) functions. Gbent functions for which it is possible to define a dual gbent function are called regular. A regular gbent function is said to be self-dual if it coincides with its dual. In this paper we explore self-dual gbent functions for even q. We consider several primary and secondary constructions of such functions. It is proved that the numbers of self-dual and anti-self dual gbent functions coincide. We give necessary and sufficient conditions for the self-duality of Maiorana--McFarland gbent functions and find Hamming and Lee distances spectrums between them. We find all self-dual gbent functions symmetric with respect to two variables and prove that self-dual gbent function can not be affine. The properties of sign functions of self-dual gbent functions are considered. Symmetries that preserve self-duality are also discussed.

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